Does Shaving affect your playing?
There is NO single answer here. It depends on your embouchure (static vs. dynamic) and how sensitive your skin is.
I played a static embouchure for years and never shaved. It didn’t bother me at all. But I did use an embouchure shift.
When I finally learned how to connect the registers and started using a dynamic embouchure I had to start shaving. The slight difference in the length of the hairs bothered me. I’m 10 times better at playing but I do miss the facial hair.
Some people have tougher skin and are never bothered by this. If the act of shaving bothers you change your shaving creme.