Tbh though you are making me uncomfortable for that matter Pixie, I think what you are suggesting disempowers women, it makes us appear weak, vulnerable and pathetic, it makes us fear things we should not fear and once that becomes normalised and established it has a knock on effect with the way men and trans women are perceived. I don't want this for womankind, it's not healthy imho.
Of course you get men who attack women, but they are not trans women, they are violent men with an agenda, and they do not represent even a fraction of 1% of men in the street, and if you think having a little sign on a toilet which says 'LADIES' means a rapist can't barge in there and rape you, then...