Why is bris a difference between a Yid and a Goy? If the goy is from ?????? or ??? ?????, he will also have a ????!
I’m not sure the answer to your question, but if i am right then your original question is back and women will not be a nafka minah, you will anyways need a new terutz!
(I once heard that the ???? of ?????? is different to the ???? we have, and a ???? was brought from ???? who showed his ???? ???? to the Brothers to prove that he was who he said he was – and if the ???? is the same, then it would be pointless. It might have to do with the fact that the ???? is done at 8 days, and ?????? at 13, but I don’t remember. [if this is the difference, you are again back to square 1, because what if a ?? has ???? after 13 or if a goy is curcumsised?])