I think the module idea is probably the most effective track, think of it as the specialty gear for boarding and storage space for looted items/crew.
Like you said, it would probably be best to simply keep the module as providing a bonus after you destroy an enemy ship in a traditional manner. Perhaps a privateer module that could only be placed on medium or smaller ships (traditionally, "pirate" ships have been smaller then those they attack, t also makes sense when you see my later points).
The module could...
1) Make the ship's loyalties unknown to enemies unless they have a certain amount of espionage against you. Just use a generic ship model for all AI pirate vessels so the human player can't tell just my matching ship color and hull design. Do the same thing for all pirate ships if multi player is ever instituted (though the player would still always see his own ship design, or the true enemy design with the proper espionage)
2) Provide a small percentage of the destroyed ship's total value to the owning side.
3) Be a relatively small module (moderately priced). That combined with the limit on ship size (you just wouldn't be able to keep the loyalties of a capital ship secret) would lend it self to creating small Pirate fleets, it would also make a player decide between earning a higher loot % or having ships that can actually overcome competent enemy ships. Picture a fleet with 4 small ships with 1 privateer module each, and two medium ships with 4 privateer modules each. If each module gives 1% (obviously the best amount would have to be figured out to help game balance) of the destroyed enemy ships value that fleet would earn 10% of the enemy ship's value (perhaps give a bonus for destroying freighters like raising the value to 1.5%-2% each) the amount earned would be subtracted from the enemy treasury (to motivate players to stop enemy piracy, if the money simply appeared out of nowhere, they wouldn't care

).
4) Perhaps to keep it the module from getting put on main line battle ships, keep ships equipped with it unable to actually destroy the enemy ship
if they with to make use of their looting ability. Simply subtract the % value stolen from the current health of the "destroyed ship" (though they would still need to fight a traditional battle, it's just that damage inflicted during the fight isn't actually applied to the enemy vessels). Could make the option to "destroy" or "loot" one of the toggle options along with defend and auto attack. That would keep players for simply using them to make money off their main warships during open war, but it would allow the same fleet to prey off of the same trade rout multiple times (and keep the number of freighter from disappearing altogether). Leave the attacked ship "stunned" for a turn or two to represent getting the ship back in running order (and to make the module useful, it would be a little odd to have a pirate fleet show up but leave their victims capable of giving chase to them).