Use the pirates as diversion / decoy
- Wait until a pirate attack and attack simultaneously with the pirates. This would split their forces and you can take advantage of their panic because they will not see your attack coming. This will also be a good pincer strategy.
- Make a deal with some pirates. Pay them, to act as a diversion and attack with the same tactic explained earlier.
- BONUS: Use your mind control magic to the pirates to force them to be a decoy. Preferably some lieutenants or the pirate captain himself because your magic is limited.
Since you overpower the port city by numbers and their strength is with naval combat, you can feed their ego by giving them what they want: the advantage they think they have.
Hopefully you have some kind of contact with the pirates because without them, the plan would fail.
EDIT: The persuasion isn't necessarily conducted at sea. Preferably when the pirates dock to some remote town to take a break. The army will not need ships to do this.
TLDR: Use pirates, split their forces