I guess losing this type of anxiety comes with age. I used to be terrified of all of these things, but what I've found is that the only person that really cares, is me. There are so many reasons that men could be shopping for women's clothing. Maybe it's a gift for someone, maybe their wife is disabled and can't shop for herself, maybe it's for a daughter. Who knows. The sales people just want your money anyway. The first time I bought them, I was in military fatigues in the base exchange before being gay or trans was acceptable in the military and even then, I never had an issue.
I do remember being terrified for the wig thing because it wasn't a store full of people. It was just me and that salesperson in a strip mall with giant windows that everybody could look into. Again, no issues. They were very helpful and I left happy. I showed up there in male mode too, so it was very obvious that I was not a woman going through chemo.
Your own self-acceptance, or lack thereof, is your biggest obstacle. Nobody else cares and the ones that do, don't matter.