I have a wife, a daughter, and 4 grandchildren, one of whom is a girl. Of course I am concerned for their safety. (As, of course, I am for my grandsons.)
But the behavior you fear is illegal whether man, woman, trans or not. Bathroom laws won’t change that. Anyone assaulting another in any restroom for any reason can be prosecuted. Simply dressing as a woman doesn’t give a license to assault women, and it wouldn’t be a viable legal defense.
Trans women are not just perverted men dressing as women. They are living their whole lives as women. They change their licenses, birth certificates, and other documents. Any man who dresses as a woman just to get into a women’s restroom isn’t going to do that, and won’t be able to show that as a defense.
Trans women don’t assault other women as a man would, because they don’t think of themselves as men. If they had that kind of aggressive male behavior, they wouldn’t be identifying as female!
Not only that, but forcing trans women to use the men’s room, puts them at far greater risk of assault from trans-phobic men.
It also means that trans men will be using the women’s restroom, which would surely make cis-women uncomfortable, too.
So it comes back down to punishing trans people for the behavior of people who are not trans!