Related analysis from Larry Niven:
Man of Steel, Woman of Kleenex
Superman used to shave with his heat vision bounced off a broken piece of mirror from his little space ship that he used to come to Earth. I apologize for knowing this. Don't ask about manscaping the sensitive regions. Ask Lois about that.
Also, (geek), if you expose Superman or other Kryptonians to red sun radiation they relapse to human level and you can then shave, get injections,etc. Sometimes they would practice H2H in red sun rooms so to be the same level as the instructor.