Fat redistribution is one of few changes from T that is not permanent. Meaning, if you'd go off T after having started it, you'd regain your former pre-T body shape, while a deeper voice and facial hair will continue to stay mostly the same. You could look into youtube vids of people who've gone off T after a longer time on it to get a better idea of how that would affect the body.
So what I'm saying is, you could go on T and reap those benefits, and it would also likely change your fat distribution while on T, but then go off T again later on and you'd get your previous body shape back while still keep most other changes. I'd also advice you to look up which T changes are permanent and which ones are not. Permanent means stays after going off T, not-permanent means they return to pre-T state when going off T.
A small however though: cartilege (softer bone-like tissue like what's in your ears and nose) grows in some areas when taking T, which can increase size of hands, feet, jaw, etc. And this change, I believe is permanent. It may however only be subtle. But any fat that moves on T would move back when off T again.
Disclaimer: I do not know if this is medically advicable, so a doc may say no to this kind of route. But in practicality it is possible and many have done it. I would not generally advice anyone to go on and off hrt, but in your particular case, it seems to me you might actually benefit from doing that. Please be careful if you'd decide to do that though.