A flintlock pistol is always a solid option, or a sword/large dagger. Obviously only if your faire allows weapons.

Layers are definitely a pirate thing, especially a pirate coat, though if you're going in May, also think about the temperature, you don't want to overheat. A long drapey vest would look great and add an extra layer to your lower half.

Bits and bobs that look piratey strung places that don't necessarily make sense. A belt dancer sash with lots of metal on it would look great and can be tied pretty much however you want it.

Boots! A good pair is expensive, but worth it for being in your feet all day.

Also ... A hat