Do you and your child really think he is not perceived as a man despite (I assume) stereotypical female hair and clothes? What happens if/when people don’t affirm him?
Who is being discomforted if your child uses male toilets? From what I’ve heard, men aren’t bothered by a bloke in a dress using male toilets, and I’ve never seen evidence of violence towards transwomen in male toilets.
If he can justify using women’s toilets on those occasions when it is not avoidable, why aren’t those reasons valid at any other times ?