When a nuke’s tiny screw pops and triggers a countdown, a guard on night duty must find and reattach it before the missile detonates.

Me too I thought immediately that this could work (only) as a short. Anyway, it is not clear what kind of action we will see in the movie/short... what the guard does? If it's a comedy (as the tiny screww suggests) then you could stress more the genre.

This would make for a great short: Mr. Bean meets I love Lucy.