Let's assume there is a Werewolf moon base, just for fun. We'll treat it as a prison camp for werewolves, which have been permanently banished from Earth. That way, all of the werewolves won't automatically suffocate and die.
The change (on Earth) only happens at night, ONLY during the full moon (3-4 days at the most) and ONLY when moonlight is unobstructed (no cloud cover). Changes don't happen during other moon phases, so the relative positions of the Sun/Earth/Moon are important! Lunar DAYS don't matter, only the relative positions of the satellite.
Inmates can function as a regular society, unfettered and not incarcerated (except that they're stuck on the Moon). Everything would be timed, and those who WISH to undergo the 'change' could be released into a special gymnasium, which would be bathed in regular moonlight during the appointed time. Everybody who wants to stay 'sane' would stay deep inside, and out of the light.
The only real question is: who governs the colony? Is it run as a prison, or as a regular penal colony, governed by 'inmates'?