Does she know how a stun gun works, or is she assuming they knock the bad guy out like in the movies? She would have to come into physical contact with the assailant (or at most 15 feet if she uses a taser). Then, if she successfully stuns him, she will have to either subdue him physically or run away before he can recover and catch her up - neither of those things sound feasible for an older lady who is scared of guns.
She will be better off with pepper spray.