Women must absolutely create a social sanction among themselves that they *must* be armed in public. “It is just something that ladies do”, is the only reason that needs be given. “And they *must* injure any man or men that attack them.”
Personally, I would suggest a bladed weapon, on the logic that women are most often attacked at very close range, it needs no mechanical fiddling, and can inflict great harm quickly with minimal force.
Social sanctions are the unwritten rules that everyone in a society lives by and enforces violations against. If a girl or woman doesn’t have a knife with her, another one might have a spare or loaner for her. Even a serrated paring knife can be all the difference between raped and dead, or not.