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Would it be possible to make a sharpie or a dry-erase marker that would work in a vacuum? Would they already work? To that end could you make a dry erase board or some such?

The problem with markers is that they contain volatiles.

You could sidestep that with older tech that uses nonvolatiles to make a mark. Examples:

1: Chalk board on slate or dark substrate.

2: Crayon or wax pencil on glass or opaque light colored substrate.

3: Pencil on light substrate.

Or use an Antigravity Space Pen like the astronauts did!

https://www.scientificamerican.com/article/fact-or-fiction-nasa-spen/

Unlike most ballpoint pens, Fisher's pen does not rely on gravity to
get the ink flowing. The cartridge is instead pressurized with
nitrogen at 35 pounds per square inch. This pressure pushes the ink
toward the tungsten carbide ball at the pen's tip.

The ink, too, differs from that of other pens. Fisher used ink that
stays a gellike solid until the movement of the ballpoint turns it
into a fluid. The pressurized nitrogen also prevents air from mixing
with the ink so it cannot evaporate or oxidize.

The article states that such pens were used on the space shuttle and in the space station, and you can buy one for $50.

Human ingenuity knows no bounds so the simple answer to your question is. Yes, No, Yes.

Simply put, if you want something to work in a vacuum, as long as there is enough incentive, someone will make it. To that end, no one is going to make a sharpie or dry erase marker work in a vacuum.

As for the No, to them working in a vacuum, sharpies and dry markers still store their ink as a liquid. The problem with liquids in a vacuum is that they will often boil then freeze. Its not about the temperature. Its just that there is 0 pressure which forces them to change states very fast. Any ink in your pens is likely to undergo a similar process, blocking the sharpie or rupturing it as the ink inside expands and solidifies.

As for the yes's. There is already a space pen that works without gravity. I'm not sure how the ink works in a vacuum, because I doubt an astronaut will worry about bringing a pen and paper with them while they are going out for a spacewalk. It would also be far more useful to record your voice while in space, or have someone else over the communication line write it down for you. If you let go of that pen, its probably going to drift slowly away form you, and you will likely have more important work to do than making physical notes when other mediums exist.