I've been looking for a while and haven't manage to find a way to do something like this:

• Round 1: you skip your attack


• Round 2: you perform an attack that is more powerful

For example it could be simulated with True Strike in round 1 but for regular weapon attacks it feels a bit underwhelming, especially if we consider off-hand attacks for two-weapon fighting.

My motivation is playing a character inspired by Duke Wuhuan from The Promise, who uses two fans and regularly sends one fan flying for a while before it lands a hit - so ideally the solution would address two-weapon fighting.

I'm looking for something based on existing mechanics, possibly with a reskin. My initial idea was based on either a bladesinger or a rogue, but there may be better ways to do this.

Consider the Battlemaster Fighter's Feinting Attack Maneuver

A Fighter with the Battlemaster archetype has access to a manoeuvre which could be alternatively described to achieve the effect you want: Feinting Attack.

When using a Feinting Attack, the Battlemaster spends a bonus action to grant themselves advantage on their next attack roll against a creature. If that attack hits, they get to add bonus damage based on their "superiority die" (so between a d8-d12 extra). You could easily describe that as preparing for an extra powerful hit rather than an actual feint.

There are some downsides - it requires the use of a limited resource, so you can't do it constantly. It also requires the target to be adjacent to you, so it's not much use at range (though you could make the feint, move away, and then attack with a ranged weapon). Additionally, though the original printing of the ability did not feature a time limit - so you could activate it on one turn and make the advantaged attack on the next - that was errata'd, and you lose the benefit if you don't use it by the end of the turn (so you can't set up on one round and hit on the next).

If your game allows feats, you can even gain limited access to this ability without being a Battlemaster by taking the Martial Adept feat, which gives you one superiority die and lets you learn two Battlemaster manoeuvres - but I would caution that this looks like an extremely suboptimal feat choice compared to the benefits of many other feats or just taking a straight ability score increase, so you would be willingly sacrificing character effectiveness just to be able to do this once per rest. I wouldn't recommend it personally and only include the option for completeness.

Bonus Option: Dancing Sword Fan

I decided to look up the media you reference to see if it would spark any further inspiration, and it did. I found a clip here which seems to showcase this fan-throwing fighting style that you reference. I think possibly the best way you could actually achieve something visually similar in D&D is to use a Dancing Sword - or at least, a fan with the same enchantment, which a reasonable DM should have no problem with allowing.

You can use a bonus action to toss this magic sword into the air and speak the command word. When you do so, the sword begins to hover, flies up to 30 feet, and attacks one creature of your choice within 5 feet of it. The sword uses your attack roll and ability score modifier to damage rolls.

While the sword hovers, you can use a bonus action to cause it to fly up to 30 feet to another spot within 30 feet of you. As part of the same bonus action, you can cause the sword to attack one creature within 5 feet of it.

After the hovering sword attacks for the fourth time, it flies up to 30 feet and tries to return to your hand. If you have no hand free, it falls to the ground at your feet. If the sword has no unobstructed path to you, it moves as close to you as it can and then falls to the ground. It also ceases to hover if you grasp it or move more than 30 feet away from it.

Basically, when you activate a dancing sword, for the next few turns it flies about and attacks people, being controlled by the use of your bonus action. After four attacks, it has to return to your hand, or it falls to the ground if you don't or can't grab it again. If you had a fan with this enchantment, it seems to me that it would look a lot like the fighting style of the character you're inspired by!

It doesn't involve giving up any attacks or making more powerful attacks, though - the dancing weapon only does normal damage as if you were wielding it directly, and as it's a bonus action to make it fly and hit something, you don't get less attacks than if you were doing normal two-weapon fighting. It does also depend on being a magic item to provide the effect, rather than it being your character's own skill, so that might be less appealing as an option.

Try this monk class feature from XGtE's Way of the Kensei.

The optional material from Xanathar's Guide to Everything includes new subclass options. One of the options available for monks is the Way of the Kensei. At 3rd level, the Kensei subclass grants a feature called Path of the Kensei -- essentially an a la carte menu of combat abilities oriented around weapons. One of those abilities, at p. 34, is:

Kensei’s Shot. You can use a bonus action on your turn to make your ranged attacks with a kensei weapon more deadly. When you do so, any target you hit with a ranged attack using a kensei weapon takes an extra 1d4 damage of the weapon’s type. You retain this benefit until the end of the current turn.

This ability appears to check off all the boxes you've identified. It involves not attacking -- specifically, not using a bonus action to attack with an offhand weapon -- in order to instead deal additional damage with the attack(s) you do make.

Take a look at Grave Domain Cleric from XGtE.

Channel Divinity: Path to the Grave
Starting at 2nd level, as an action, you choose one creature you can
see within 30 feet of you, cursing it until the end of your next turn.
The next time you or an ally of yours hits the cursed creature with an
attack, the creature has vulnerability to all of that attack's damage,
and then the curse ends.

Effectively, you spend one turn setting yourself up for an attack that is twice as powerful the next turn. From a flavor standpoint, this is less of you powering up and more weakening the enemy, but it gives the same effect as a powerful strike the next turn. Since it's you or an ally, unless you want a party member to swoop the vulnerability, your should hold this action until just before your next turn.

Smite Spells

Some other Bonus Action power-ups you could look at (going off Carcer and screamline's answers) are the Smite spells. They all work as a bonus action that adds damage to your next hit and an effect if they fail a save.

Searing Smite: 1d6 extra fire damage, sets creature on fire. (1st lvl)

Thunderous Smite: 2d6 thunder damage, pushes creature 10 feet. (1st lvl)

Wrathful Smite: 1d6 psychic damage, causes fear. (1st lvl)

Branding Smite: 2d6 radiant damage, creature loses invisibility. (2nd lvl)

Blinding Smite: 3d8 radiant damage, creature becomes blinded. (3rd lvl)

Staggering Smite: 4d6 psychic damage, creature gets disadvantage on attacks (4th lvl)

Banishing Smite: 5d10 force damage, creature is banished if it ends with 50 or fewer HP (5th lvl)

An Oath of Devotion paladin could work.

Round 1, use your action on the Sacred Weapon Channel Divinity option. This gives you a bonus to hit equal to your Charisma modifier for 1 minute with a weapon of your choice.

Then use your bonus action to cast a spell like Wrathful Smite, Searing Smite, or Branding Smite. The Paladin has several of these "Smite" spells to choose from. These spells don't take effect until the next time you hit with a melee attack. For the most part, they add damage and an additional effect to the attack.

Round 2, go in for the attack. Your Channel Divinity should help keep you on target. If you prefer one massive blow, add a Divine Smite onto your first attack to get the effect of both your spell and some extra radiant damage. If you want to play up the dual-wielding, you could save the Divine Smite for your second attack and roleplay that each weapon has a different effect.

You're limited by spell slots and 1 Channel Divinity per short rest, but I think this covers what you're looking for.

In response to screamline's comment: If you prefer to stay at a range, you could substitute the "Smite" spell for Divine Favor or Magic Weapon. They don't have quite as much oomph, but the option's there. Divine Favor lets you add 1d4 radiant damage to all weapon attacks for 1 minute, and Magic Weapon turns a nonmagical weapon into a +1 weapon (up to +3 when cast at higher levels). Either can be cast as a bonus action.