I've never had an in-person play exam, but that doesn't stop me from thinking about how the ideal exam might be conducted.
If embarrassment is what you're after, then I agree that boxers don't really do the trick for me. They're not embarrassing or humiliating at all. The only time I'd think they would be good for a play exam would be if you wanted to embarrass the patient by having an exam that they weren't expecting at all. In that case, showing up for the exam in boxers might be more realistic, and then you would embarrass them by quickly removing them.
For a good embarrassing exam, I would opt for briefs, preferably white and tight. They naturally draw your attention to those male body parts that aren't supposed to be displayed in public.
But for an even better exam, I'd go with a nice jockstrap. Like briefs, it naturally draws your attention to the male genitals and it grips them even tighter. But often the front pouch is made of an elastic, mesh-like material that can be almost see-thru depending on the brand and style. That combination gives the patient the impression and feeling that they're covered (at least in front) but that may not actually be the case due to the see-thru properties of the pouch. So their doctor can see all of their naughty bits in front without them realizing it.
And then there's the bare-back of the jock. It's obviously the most prominent feature of the garment. It suggests that the male wearing it is deliberately presenting their bare ass in preparation for some activity, possibly for penetration, which would "normally" be considered taboo for a male. And when you combine that with the tightly-bound genitals in front, it's almost as if the male is wearing something that is uniquely designed to present them as totally submissive. The front is tightly bound, so the male is not able (or allowed) to penetrate someone else, and their ass is bare and on display. Just the opposite of what society would consider "normal" for a male. It's as if they're just begging for someone to bend them over and fuck them up the ass right there. And in my mind, that's perfect for an exam where they will certainly receive (at a minimum) a good rectal and prostate exam (perhaps even more than that).