Most aerospace medicine is through the military (AF, Navy). I was considering the HPSP for a while and a recruiter was able to set me up a visit to a base to meet with a flight surgeon.
I'm not sure how that would work with shadowing, but it can't hurt to ask. Do you know anyone in the Air Force or Navy? It might be easier to work it through a mutual contact on a base than to try to contact a physician yourself.
Sorry, I couldn't be of more help. You might check the military medicine forum for more info about flight surgeons.
Maybe someone else on here has experience with civilian docs.