After posting my comment, I googled "how do astronauts shave in space." Among the many results was this video:Oh. He/they just wiped the stuff off on a towel.
ISS, I'm not sure. Electrics I think.
AA
It turns out astronauts use both electric razors and cartridge razors. The electric razors are preferred by some because there's no need for water, but it does make me wonder how the razors capture the shaved beard hair with no gravity. For the cartridge shavers, there is an astronaut shave cream. I wonder if it's just Cremo in a tube.
If I were in charge of PR for one of the cartridge companies, I would be touting my products as out of this world!