Helpful hint: Your MD can prescribe a cream that's used to treat them and does a good job of reducing the sensitivity factor, I used it once and it helped.
I also think it's lunacy that airport security has us worrying about things like this. To note, I have had a pat down that was that invasive. If you spread your legs and have muscular legs as I do, it's naturally easy to hit the spots the OP is worried about.