I have lived both of those scenarios in my life and I can assure you the latter is much more pleasant. The first happens not only to people who dress as the opposite sex but also to transitioned women who don’t always escape scrutiny either through certain physical traits, voice or mannerisms. It also happens to anyone who doesn't fit into a cookie cutter mold of conformance whatever their difference may be.
What was the biggest change in me that allowed me to pass from one stage to the other? my own attitude which is ultimately the only thing you can control. I was simply tired of worrying about what others might think. The alternative is to live in fear in a world that is full of people just waiting to pounce and you only give them power by simply showing that fear.
This change needs to happen in your psyche because it is not about feigning confidence but about having it and must form part of a self-acceptance process that says “this is who I am take it or lump it”.
As soon as that knowledge takes root, you will notice the dramatic change which will allow you to take ownership of your identity.