If i lose weight while transitioning, will it help me disguise my breasts?

Things are currently a bit awkward between my wife and me because after a lifetime of wanting to resolve the unhappiness i have as a result of having a male body, which she's known about since the start of our relationship, i am finally taking hormones, and of course one of the results of that, which i personally find very positive, is that i am slowly developing breasts. However, my wife finds this prospect disturbing. If i simultaneously try losing weight while they grow, is it likely to make them less obvious to her? I understand her difficulty with the prospect and was wondering if this would help. In an ideal world i would just let them grow, but it doesn't look like a viable option i'm afraid.