there is no information about how widespread the practice of humans adopting dwarf customs and status might be, so there's no way to tell.
However Nanny Ogg's putative dwarf ancestry, Casanunda's activities and Carrot's generally-accepted dwarf status and probably clean-shaven appearance combine to suggest that there is a generally-understood ettiquette covering the matter.
Carrot doesn't carry an axe, either, although dwarf officers in the Watch appear to carry axes rather than swords for cultural reasons. There is no mention of Pepe having one. Grags don't appear to carry axes, at least the deep-down sort, and nor does the 'modern' grag in 'Thud!', at least as far as can be told.
So, I'd suggest that both beards and axes are cultural icons which can be modified or disregarded as the occasion demands; whereas from various comments by both Pepe and Carrot, making the necessary observations and rites is very much compulsory.
Which all fits in with dwarf society being essentially Jewish in character. You can be born one, and you will always be one; or you can become one by conversion, although the degree to which this is accepted varies. Their marriages are monogamous and contain various contractual elements; it would be interesting to know if their households are matriarchal, since their women are certainly not discriminated against or constrained legally.
Minty Rocksmacker is clearly female and known to be such, and her silky beard is specifically remarked upon. I'd tend to regard the whole 'Minty' issue as one of those continuity glitches which have been simply dropped for the sake of subsequent plots, though. Casanunda could also be in this category.
