Cockroaches don't live up to their reputation.

The domestic cockroach that seems so hard to kill is as dependent on our warm comfortable environment as we are. If you want to clear an infestation in a cold climate, just leave the heating off, the windows open, and go away for a couple of weeks. The cold will kill them all off.

Locusts on the other hand do live up to their reputation.

As long as the local flora is edible and the temperature is within a suitable range, locusts will breed to plague levels and devastate the vegetation across vast areas.

Cyanobacteria

Also known as blue-green algae, while often not blue-green and never algal, these bacteria are possibly one of the oldest forms of life on the planet. They photosynthesise so you don't need to worry about local life forms, any nutrients will do, they really like nitrogen rich water. In effect they range from skin irritant to neurotoxic, they also have a tendency to form massive blooms in fresh water leaving it poisonous to many animals.

Cockroaches and other animals need food. It is very unlikely that planets around galaxy will have life forms that are compatible with us - even on our own earth many organisms can't digest cellulose and mycochitin, and on other planets evolutionary paths will be totally different and unrelated.

What you need is something with photosynthesis - simple plants, cyanobacteria, generally low level pioneer species. That would at least give them a chance.

Chemo and radiosynthesis, and other possible forms of making own nutrients are risky, you can't really be sure there will be appropriate energy source available. Light is pretty universal, so it is a safest bet.

It is unlikely for something like this to work

Your falling point here, like pretty much all questions about alien fauna/flora, is Chirality. If the planet your cockroaches land on has the wrong chirality, the cockroaches will not be able to derive any nutrition from eating the flora/fauna, and may in fact have lethal allergic reactions to it, quickly killing off your pests.

This is, of course, passing over the issue of maintaining a breeding population of cockroaches whilst they travel the depths of space, or the inherent problem that if the cockroaches eat 99% of the local flora/fauna, your cockroaches will have no more food and starve, potentially leaving some remote natives alive to repopulate.

It'd be much more efficient to launch a set of Von Neumann Probes to hunt down and eradicate life. Just make sure that the kill switch is the last thing to mutate though, unless you want to become a cautionary tale after your robots sterilise your home world.

As @Kieran mentioned in a comment, a way to use Von Nuemann Probes whilst sticking with the DNA theme would be to have them analyse the environment, before designing and manufacturing a set of invasive species (specialised for this world) to destroy the natives. Perhaps your probes could collect the DNA and use it for later invasions, producing your own Tyrannid Hive.

First problem.

Animal life is a parasite on plant life.

Cockroaches breathe oxygen released by photosynthesis, consume plant matter that was created by photosynthesis, eat animal matter that in turn was fed by plant matter created by photosynthesis.

The animal isn't capable of building its own nutrients, but rather relies on the complex organic molecules the plant has built. In an ecosystem that the animal did not evolve in, the organic molecules the plants use (for structure and energy etc) could very well be completely incompatible, leading to animals with in turn completely incompatible biologies.

If you consider this unlikely, the story of trees and coal should fix that. Trees (and hence wood) evolved many millions of years before organisms that could break down wood did. So huge piles of unrotting wood built up. These huge deposits of carbon are what most of our coal deposits are made out of.

Millions of years later, white-rot fungi finally figured out how to rot wood. And it stopped happening.

Our life forms co-evolved to eat each other.

The cockroach could arrive, eat things, and find nothing provides it with enough energy or nutrients to live. What more, everything could be poisonous or toxic to the cockroach.

Macroscopic life on Earth is relatively recent, and it exists in a specific kind of life-modified world. A different biology or ecology could easily result in an atmosphere poisonous to cockroaches and organic matter it cannot get energy or nutrients from.

Second problem,

Space is big

Firing stuff in random directions in space won't hit planets. Hitting a planet (besides Earth and the other planets of the Solar system) by firing in a random direction would be like firing a gun in a random direction, and hitting a specific target on the other side of the planet, 1000 times in a row.

Gravity won't "pull you into" planets, but would almost always just swing you into a new direction.

Next problem,

Stars are far apart

Launching something at a speed that it would reach the other side of the galaxy before, say, the Earth is swallowed by the sun, requires insane amounts of energy and technology.

Stopping such a projectile requires you to package insane amounts of technology and energy into the projectile, which is exponentially harder.

And then we reach:

The Galaxy has lots of stuff in it

Suppose you have perfect aim of star wisps. If you fired one per star, that is 100 billion stars.

We are already talking about a task that the entire human civilization couldn't pull off once, and you want to do it 100 billion times.

You need to rework your plan.

Start with a star-wisp based self-replicating mini civilization. This is already insanely hard, technology wise.

You launch a dozen or so of such wisps. They fly to nearby stars, quickly check for raw materials. If they see it, they stop. They then try to bootstrap their own industrial civilization.

After, say, about ten thousand years, 1 in 10 of them have the ability to launch star wisps in turn. Each launches a dozen wisps, at a rate of 1 every hundred years. (These are expensive to launch!)

So every ~10,000 years, you get 1.2 times as many wisps as you had the previous cycle, and start with 12.

To reach 100 billion wisps this takes 139 cycles, or just over a million years.

In practice, you are going to be more limited by the speed of light than replication rate; the galaxy is 100,000 light years from end to end, and your star wisps are probably moving slower than 0.001c (get going faster than that, then stationary atoms in the interstellar medium hit you like hard radiation. Not good). As with all exponential growth functions most of the growth happens in the last part, so after the local corner of the galaxy gets saturated you'll have a relativistic speed (even 0.001c is relativistic) wave of star wisps leapfrogging each other to colonize every system it can.

This star wisps armada can then build simpler things, like customized biological weapons, to disrupt any ecosystem it finds. However, more likely and usefully, it could instead seed dead worlds with life, or even try to redirect the ecosystems of worlds towards complex multi-cellular life and/or an oxygen atmosphere.

What more, 3d printing a human is a simple task compared to creating star-wisp producing civilization. So the armada could switch from spreading to invasion after it sets up a beachhead; the invading biologicals could be printed humans.

This will likely not work with any higher organism

Cockroaches as much as any higher organism from earth is much more dependent on an earth-like biosphere, thus your plan would only work under the assumption of a biosphere similar enough to earth to nourish and shelter your neobiota and these have to be tougher than the local organisms adapted to the eco system.

Viruses

Viruses may have adapted to Earth DNA, but retroviruses are still the most versatile and flexible creatures (lifeforms or organisms would not be correct here) we are currently aware of. If the alien way of saving genetic information is so much different that a cocktail of any virus known on earth (and possibly lab-engineered mutations of these) does not have any effect, no earth-stemming organism would have a chance to survive or reproduce at all, as they probably could not even digest local fauna or flora.

An assortment of fungi

Fungi do not necessarily need oxygen to live. Some are optionally aerobic, so when they invade an ecosystem and overgrow there, they may compete with the local fauna for oxygen. For air breathers there might be little to no impact, but for water dwellers this will spell doom.

The fungi may also grow unchecked and deny light to local flora.

Unlike viruses fungi will have no problem adapting to local life. Where there is a substrate for the fungi to feed on, there is a way.

Finally, the way fungi grow and spread is a marvel of biology. Some like cordyceps start their life as single celled organisms, which then fuse - yes, fuse - into a single chimeric organism shaped like whatever beast it is that they are feeding on from the inside. Others grow to gigantic proportions - a single individual armillaria is over five kilometers wide!

Even if every other aspect of your plan worked (it doesn't, see the other answers), your last step would probably still fail.

I'm talking about this "kill switch" you installed. The problem are random mutations. In the best case scenario you have somehow colonized 100 billion star systems within less than 100 thousand years (assumes you spread at light speed starting from one edge of the milky way). For every colonized star system you will have a billion or so cockroaches. So your kill switch must have a reliability of better than 1:100 trillion over 100 thousand years.

Those are really long odds. All it potentially takes is one small enough population to survive the kill switch on some backwater star system and who knows what will happen...

One might suppose the emperor knows where the target planets are. Otherwise, the logistics wouldn't work out without the probes like Kyyshak mentioned.

If the hostile civilization is more familiar with the target, it could be possible to engineer the offensive species for each target before sending them. In that case, viruses are still the best bet. Larger organisms might seriously disrupt an ecosystem, but they are unlikely to completely overwhelm local life forms.

If you insist on larger organisms, I recommend a duplicate of the target species. These duplicates can be designed with reproductive advantages, breed with the population and spread the kill gene in the target species.

A cocktail of retrovirus' and bacteria.

Have several hundred strains of virus' that are programmed chlorophyll producing cells, bacteria, algae ect. The bacteria are programmed to consume any and all biological material it can. Pretty much go for the bottom of the food chain. These are also programmed to a very quick life cycle, multiplies quickly and adapts to any environment possible. And programmed after a set amount of time to target itself and/or turn off it replication ability.

This cocktail would be designed to consume oxygen and eliminate oxygen producers. Soon, much of the complex life would die out, leaving little to stand up against the Empire.

This is followed by another cocktail that is designed to restore the planets atmosphere and clean up anything left behind from the first wave. Maybe have a third wave to ensure a clean reset of the biosphere.

This wont kill all life, but would make it significantly easier to colonize as there is no mega fauna to deal with, except the ones you bring with you to repopulate.

If, as others have mentioned, that the adaptation of your biological genocide bugs gets out of had or fails to perform, drop an asteroid on the planet and say "screw it."