That sounds like just the set up that I had in mind.
I spent several years in the US Navy. Our Ship's Troops were 2nd class Po's and 3rd class mostly from different division's in weapons department. Their job was ship board Security. There was also a ships self defense force lead by the Gunnery Officer and the Chief Gunners Mate. the fire teams in the SDF where lead by gunners mates. the bulk of the Defense force were unrated crew men. the ship Defense force was tasked with boarding actions ours never had to.