Instead of actually stealing the trigger watch from Kyle, the player character could devise a way of disabling the trigger. One way is to sneak up on Kyle when he's sleeping and use the mechanic skill on the trigger to disable it, thus not risking waking Kyle while trying to remove the watch. Another way is to use the science skill to devise a way of rendering the signal in the trigger watch useless – some kind of frequency jammer made from the parts found in the Rocket Assembly Building. Either solution would allow them to grant the Bear freedom, clear the path for either Bear or the PC to become leader, and/or make Bear a CNPC.
Character type completion breakdown
Combat Boy – All boils down to whether or not the player has put enough points into mechanic or science. If not, then a possible alternative is to get Jillian to disable the trigger, provided the prisoner retrieval quests are done and the player didn't piss her off.
Diplomacy Boy – Same as Combat Boy, but player has the option to try and talk Sid into doing the deed.
Science Boy – Another shining moment for Science Boy. The skills are his, make good use of them.
Stealth Boy – This would help when sneaking up on the sleeping Kyle, but after that, it depends on how much was put into mechanics or science.