A couple of thoughts from a TSA skeptic.
If you have a sling without metal? If so use that.
With the sling, they should realize that you can't "assume the position" required for the millimeter wave scanner, they should direct you to the walk through metal detector instead.
Assuming that you do not "alarm," the procedure is to swab you hands, and shoes if you keep them on. No hands on body feel.
DO NOT say you can't or do not want go into millimeter wave scanner. If you do that, you are likely to be considered an "opt out" and then definitely get the hand search.
Like Wheeled Traveler, I go with the search me in public. I figure the security screener is more embarrassed grabbing "my junk" in public than I am. And it never hurts to have witnesses.
Unlike WT, I have had some bad experiences with screeners hurting me when I tell them where I have pain. I guess some feel that I'm hiding something there.
Good luck.
On the editorial/opinion side. Although they wear badges, they are not law enforcement officers . . . and "...just trying to do their job..."? Really?