Here’s my solution:
1. Let them pat you down publicly.
2. When they get into a sensitive area, give a little jump like a hair got caught in a zipper and say “Ow!” loud enough that others nearby can hear it.
(BTW, there’s no scientific basis whatsoever that these body scanners are safe. No research. No testing of animals over long periods of time with larger radiation doses. Nothing. Nada. Zip. The Feds are just saying that. “Oh sure, of course it’s safe. I’ll opt for the public patdown plus a little theatrics. But mainly I’ll opt not to fly at all any more.)
EPIC.org is a good start about this and other issues. Note news items at end of link.