De,
Just tell them you are seriously concerned about the radiation danger.
If they attempt to reassure you instead of simply accepting your preference tell them YOUR GOOD FRIEND'S RADIATION HARDENED MEDICAL DEVICE has been FRIED by their machine so you KNOW the energy levels are pretty high and you simply don't want the radiation exposure.
I didn't have to explain anything. I just said I didn't trust their machine and wanted a pat down. The TSA agent, who actually was a fairly cute female, immediately agreed, saying something like "I understand, honey", barely touched me, and waived me through. It took arguably LESS time than going through the machine. I guess that time could change if more people wise up or it is a bad day or you get a jerk or you are wearing heavy clothing. It probably helps to wear relatively tight clothes; I was wearing jeans and a tee shirt -- not much room for anything to be hidden except up my butt, I would think.
Don't make it sound like a protest; make it a statement of concern about unnecessary radiation exposure. No decent, intelligent person has any right to harass you about that concern. No informed and intelligent person, imo, should accept the risk for the sake of convenience; most especially not the TSA's convenience.
I suspect those new machines were largely about payout to some more of the insiders. I heard the former head of the TSA became the CEO of the company which makes the new body scanners and the new scanners were "coincidentally" approved right after he took his new job. Nothing happens by coincidence in the realm of politics & government.
I have come to realize that men are not born to be free. Liberty is a need felt by a small class of people whom nature has endowed with nobler minds than the mass of men. -Napoleon