... wonderful, and dramatized, view of Titan ICBM silo crew change and launch sequence.
Yes- the officers in the silo command capsule were armed. In fact, as per Gen. LeMay's orders, all SAC personnel who had anything to do with the 'immediate-vicinity' storage, maintenance, arming or use of nuclear weapons carried firearms. Additionally there was the 'two-man' rule which dictated that nobody ever went anywhere or did anything without another qualified team member at their side.
Interesting to note that in the movie the launch officers are issued old fashioned .38 caliber revolvers. Not the standard .45 automatic pistols one would expect in a military environment. This may be small piece of amazing technical accuracy on the part of the film makers. An automatic pistol, with it's spring loaded magazine was prone to jamming if not properly maintained. These officers sidearms are treated as just another office item like paper-clips of ballpoint pens.
A simple revolver will always fire.