Silver Age Superman didn't have to shave. His hair and fingernails didn't grow when he had his powers. One time he got stuck in the far future when the sun had turned red, so he had to make sure to cut his nails and hair and shave right before he returned to the present because he wouldn't have been able to do so once he got back.

I'll have to watch that video later when I've got time.

"It is a remarkable dichotomy. In many ways, Clark is the most human of us all. Then...he shoots fire from the skies, and it is difficult not to think of him as a god. And how fortunate we all are that it does not occur to him." -Batman (in Superman/Batman #3 by Jeph Loeb)