I too wear a prosthetic device. I wear a colostomy appliance. They have to see it and swab it for explosives, which I understand and support..
I actually prefer going through the body scanners now because the process of failing that is much quieter--just agents talking into their arms via ear pieces--than the alarms and yelling that comes with the metal detector..
I believe you may not have a choice on the secondary screening being in public. One time I was hauled off into the private room and not given a choice. The second time they started doing it in public before I asked for a private room. The differences was that the first time the failure on the body scanner--and they tell you where it fails--was in the groin region and the second time they decided it was in the waist region. I was wearing the same appliance in the same exact spot with the same type of underwear three days apart..
The appliance did not move but the agents interpretation did. The bag was fuller te second time, but still the bottom of it is most definitely in the pubic/groing region. It was amusing something that did not move was in different regions of the body to different agents. .
If your prosthetic attaches at the hip bone, they will probably force a private screening on you. The pat down itself is not too bad in terms of the crotch touching, but they really focused on my bag through the pants the time it was in the groin region..
That is really bad, as it got the clip stuck on my underwear; this happened because they couldn't see what they were doing. Thankfully the force was low enough to avert disaster. Still, it was extremely uncomfortable. .
The second time, they had me expose it and touch it myself then they swabbed my hands. This was much preferable to risking a leak because some agent can't see my bag and doesn't know where the trouble spots are.
From now on, I hope they use the expose and swab procedure. It is much more comfortable than a pat down which could cause a leak..