A Star Control Cloaking Device?
I have no idea what ship designs are in the game, but am fairly confident they have the initial designs for them already. There would be many ways of making a cloaking device work in Star Control as a permanent secondary system. I personally think the best and most fun way would be a cloak that only lasted for 2-4 seconds or so. The ship would have a fairly powerful but short ranged weapon. The cloak would then have two uses, offensive and defensive. Against faster more maneuverable ships it would be used defensively to make a turn the enemy cannot see. The cloak ship disappears, then re-appears a few seconds later still nearby but heading in an unexpected direction. Against ships with powerful or medium range weapons it would be used offensively to close the gap between medium and short range to use it's weapon.
This is simple enough to work in this type of game and provides real, easy to understand uses for it while the short duration prevents it from being a god-like ability. You can use it to evade, or you can use it for a brief moment of protection on an attack run and these abilities are probably in-line with the secondary abilities that exist with the ships you have.