I'm not worried about how I look or the pain, it is the intrusion, I think, like you said. Not even the physical intrusion or the mechanical act, something different still, it's the entire experience...maybe it's a trust/vulnerability thing...opening up to someone who is there to judge your health level* and in an unequal relationship, someone you haven't let in. I'm just thinking...the stressful factor is definitely the presence of and relationship with the doctor for me. For a stranger to see my bodied-ness (not the actual body, but a concept in my mind)...is stressful. Pap smears are probably a good exercise for us that way.
*I dunno, I feel responsible for my own health. Like if something goes wrong it's my fault. I could have eaten better, I could have gone for a check-up sooner, I could have known (because I always think of the worst case scenarios, hi, Ni) etc. etc. Is this inferior Se...need to control the Se environment?
I always dread it and try to occupy my mind with other stuff. It's a completely irrational fear. After all they are there to help you. Writing this out certainly helped me! That and actually telling people how you feel about it...my ESFJ mother is pretty level-headed about it...works well.