If this law will allow this only to transsexual people, then I would support it.
Transsexual, transgender.
Its all the same to me
A person who dresses and behaves like the opposite biological sex is a transgender person.
A person who not only dresses and behaves like the opposite biological sex but has also underwent a surgical procedure and hormonal treatment is a transsexual person.
I hope you're aware that no one is going to accept your arbitrary definitions just because you say so. Hell, we don't accept the left's arbitrary language changes, so no reason we should make an exception for you.
A person who accepts their biological sex, but just enjoys dressing like the opposite sex, is a cross-dresser. Archaically, they were known as transvestites. A person who identifies as the opposite sex - or, as I usually put it, playacts being the opposite sex - is transgender, whether they've undergone medical procedures toward that goal or not.
There frankly is no purpose in trying to introduce new distinctions, and it certainly doesn't help communication in the slightest.