I think that it is permitted based on the idea that shaving with a razor is forbidden, but not other ways of removing facial hair. (It’s been a while for me, but see last perek of Makkot -Mishnah on 19a; Gemara on 20a and see Yoreh Deah 180-182 one of those simanim).
The concept of begged isha only applies to removing hair where women (could) normally remove hair – underarms and below the belt (again see Yoreh Deah in about the same set of simanim).
From Makkot 20a:
?”? (????? ??) ???? ???? ?? ????? ???? ???’ ???? ??????? ??? ???? ?”? (????? ??) ?? ????? ?? ?? ????? ???? ?? ???? ????? ??????? ??? ???? ????? ???? ?? ????? ?? ???? ????? ??? ?? ????? ??? ???? ?? ???