That's the approach I plan to take even if I do Cardio and get all hot and sweaty. Of course right now I'm not going to the gym as Alyssa for two reasons. One, my membership is still registered in my male name and with my male photo so they may not even let me in the front door. Two, I don't have enough of my own hair grown out yet to do anything feminine with it and I don't want to get all hot and sweaty under a wig or risk having it fall off while working out.
Once I am to that point, I plan to avoid using the locker room. While my gym has a track record of supporting trans rights and our ability to use the proper locker room, I don't want to do that until I feel I'm not likely to get clocked. Bathrooms are one thing, women don't generally walk around naked in them. I just feel like they'll be far more sensitive in a locker room where they are showering and some have no problem walking around openly in their birthday suits.