Your Obedient Serpent shaves, by preference, in the shower, sans mirror, and has done so since finally abandoning his electric razor almost a decade ago.
Not only do I rarely cut myself, but I maintain a neatly-trimmed goatee. You can do a lot by kinesthetic sense and just feeling your face to find any spots you've missed. I'm sure that blind people quickly develop the same skills. The idea that the lack of a reflection would be such a handicap in shaving even after eight decades struck me as sufficiently absurd as to warrent a comment.