Sometimes when I'm deployed I'll have a dry room (dry CHU). I always take a small mirror and a big stainless steel bowl for my shaving kit. That way I don't have to worry about burning someone else's head time. That bowl, a towel, strop, razor, bottle of water, tooth brush and the mirror and I'm set. Wiping the razor on a piece of news paper helps to keep the water in the bowl clean for the face rinse.
Regards
Chasmo