Shapewear that constricts but doesn't offer extra padding in feminine spots exists. It's not really for me, for a variety of reasons, but there's no shame in wearing it if it makes you feel better about your body.
That said, like everyone else, you're pretty much stuck with your body type. Your belly is going to be there, exactly the same size, regardless of what you do with your chest. Going without a binder might make it more socially acceptable because women aren't under quite as much pressure to be physically fit, but personally, I'd take dealing with average insecurities over dealing with being misgendered any day.
