Well I was as wrong as can be. Just watched the movie 'Apollo 11' which is shot using all original footage. These guys did indeed shave during the mission. There was a piece of footage showing one of the crew shaving on the return journey using what would appear to be the TechMatic.Now I wouldn't call myself in any way NASA qualified but...If the subject of shaving in space came up, especially during relatively short missions, I would say just don't shave. If maybe, I dunno, these astronauts insisted on shaving, or there was an insistence by top brass that they should return clean shaven, just for the photo opportunities like...well I would suggest a Schick injector with one blade pre loaded prior to launch.
Personally I would be surprised if these guys put anything on board that wasn't needed, or deemed necessary for emergencies. But I'm not NASA.