i agree, pirates should extort, and/or capture ships alive. Destroying things simply isn't profitable, they shouldn't be doing it without good reason.
This can be modded however I'm unsure of the impact it would have on a game long-term. You could add the Scavenger ability from the Snathi DLC to the Pirate faction allowing them to occasionally capture any ships. Unfortunatly, In order for them to use special ships like constructors you may have to edit the AI a bit as they only seem to use colony ships (I can't help you with Ai editing in Gal Civ 3 yet but i remember seeing a post or 2 about it in the forums somewhere).
You will need to edit the Pirate Faction at the bottom of FactionDefs.xml by adding the following line:
to the faction where RaceTraits are Defined
You could also create your own ability based on the Scavenger ability instead to change how often they capture other ships, the scavenger ability is found in \Galactic Civilizations III\DLC\DLC3_Snathi\Game folder rather than base game folder in the file DCC3_AbilityDefs
Pirates should have hidden bases on asteroids. It doesn't make sense that they have shipyards floating in the middle of no where.
They should also be a galaxy wide faction that trades for tech.
The pirate faction ship style uses asteroid bases for their star bases and you could use the above method to allow them to capture and use constructors.
If you want to just change the look of the shipyards they use you could either create a new one and replace the current shipyard or you could replace it with one of the pirate starbase designs. Keep in mind that this will replace the shipyard for any faction using the default Pirate shipstyle. To avoid this I would recommend making a copy of the default pirate shipstyle to make your changes on with a new name, then editing the Pirate faction in FactionDefs to use the new shipstyle.
Info on creating ship style sets can be found in the following links: