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.
Pops
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. This site Trumpet College is about; Trumpet lessons and trumpet books by Clint 'Pops' McLaughlin - All major embouchures taught. Learn how to play effortlessly based on your facial structure. Thousands of students helped from serious amateur to pro level. Check out our trumpet lessons, our online trumpet lessons and our trumpet books. Trumpet playing, trumpet lessons. This site covers these topics: trumpet playing, trumpet lessons, Stevens, Superchops, Maynard Ferguson, mouthpieces, Bach, Callet, Schilke, Doc Severinsen, Yamaha, Maggio, embouchure, trumpeter, trompette, trompeta, trumpeting, marsalis, louis armstrong. Thanks for visiting.
Pops