Is certainly extra hoops but looks like the payoff may be worth it.
The concern angle is also nice assuming it's genuine.
Could also be nice to have them agree in the end to give further validation of who you are to anyone who doubts.
Not that you need it of course you are you no matter what but it can be used against those who need help accepting you (those you decide that are worth the effort not just anyone).
Might be a long shot but would he accept a compromise that you'll see the other therapist once you've started HRT?
After all the other therapist could cost you precious months and if his concern is genuine he shouldn't want to hurt you by making you wait longer than necessary.