Percy as a pirate captain would likely have a ship with special features. It could be enchanted in some way, perhaps having the ability to sail faster than normal ships due to some demigod - related magic. His cabin on the ship might be filled with mementos from his previous adventures on land, like a trident he once found or a piece of armor from a defeated monster.
In the fanfiction, Percy might face off against other mythological creatures while at sea. Maybe he has to deal with sea serpents that are causing trouble for his ship. His sword - fighting skills, along with his powers, would come in handy. He could also form alliances with other demigods or mythical beings who have an interest in the high seas.
It could be the navy. They see pirates as outlaws and would be determined to capture Percy and his crew. They might have better - equipped ships and more trained soldiers, making them a formidable foe for Percy and his fellow pirates.
There are likely many interesting elements. For instance, the setting on a pirate ship would bring a lot of details. The creaking of the wooden planks, the smell of the sea and tar. And Percy might have to deal with the pirate code, which could lead to all sorts of moral and ethical dilemmas as he tries to balance his own values with the rough and tumble pirate life.
Maybe an ancient sea demon that has possessed a pirate captain. This possessed captain is now leading his crew to cause chaos everywhere. They are attacking other pirate ships and even some demigod - related places. Percy has to find a way to exorcise the demon from the captain and stop the crew's rampage. The demon is very cunning and uses the pirate's knowledge of the sea to its advantage.
Percy could be a pirate with a wild and carefree attitude, always ready for a fight on the high seas. His powers over water would make him feared among other pirates. Annabeth, on the other hand, would be more refined as a pirate. She'd use her knowledge of architecture and engineering to improve the pirate ship. For example, she could design better defenses or more efficient storage for loot. She would also be the one to keep Percy in line when his pirate ways got a bit too reckless.
One idea could be that Percy and Annabeth are on a pirate ship, and they discover a hidden treasure map. They have to battle other pirates and sea monsters to reach the treasure. Another could be that they are pirates who are trying to free a group of captured demigods. A third idea is that they are pirates on a quest to find a magical artifact that can control the seas.
One idea could be Percy discovers a hidden pirate ship in the middle of Camp Half - Blood's lake. The ship is cursed and Percy has to team up with some pirate ghosts to break the curse. Another could be that Percy is transported back in time to the golden age of piracy and has to find his way back while dealing with pirate villains and sea monsters.
Well, perhaps the fanfic could start with Percy and Annabeth being magically transported into a world of pirates. They are initially confused but quickly realize they need to work together. Percy might be a natural at sword - fighting on the ship, while Annabeth tries to figure out the politics among the different pirate crews. They could be on a quest to find a magical artifact that the pirates believe will give them ultimate power over the seas.
The main antagonists could be other pirate crews. There might be a particularly ruthless pirate captain who wants to take over Percy and Annabeth's ship and all the treasures they might be after. This captain could be jealous of Percy's powers and see him as a threat.