Peep, I understand that worry completely. If I have to do anything more physically exerting than walking up stairs, doing it in a binder is awful. I was helping move a new roommate in yesterday, so I couldn't wear it and opted to wear a baggy hoodie on a really warm day instead. And then I had an awkward moment where I had to take the hoodie off because I didn't want to ruin it.
If it had just been the new roommate at the time, I would have been fine, because he's trans too. But he had a friend over. And despite wearing a teeshirt, I felt more exposed than if I'd had my shirt off entirely. It was the first I'd felt anything like that, too. It was a strange moment. But still, I suppose better than trying to wear my binder while hauling boxes around and passing out.