Agreed, I also thought about the possibility of just removing the computers vs. turning them on. However, that's a little more easily shot down by the Warden... if they're terminals, they might not actually contain the data at all. If the players don't know where the hard storage is, or if it's decentralized throughout the ship's networks, that plan doesn't work.
Edit: In fact, if my players wanted to do that, I'd let them go crawling through electrical conduits to try to find the central data storage but make that where ALL the rats live.