I think this depends a lot on where you live.
In Europe, a handshake is mandatory (if air kisses are not made), but you may give this handshake from a seated position if en femme.
In the US the handshake or air kiss is not mandatory, but if not offered, the doctor will most likely judge you accordingly. If not proffered, the doctor will rank you among the socially uneducated, and treat you accordingly. But he will never let you see his opinion. And it matters only if the doctor thinks that the socially educated deserve at bit more detailed attention in the operating room.
At least that is what my doctor friends tell me. There is the myth of should, and then there is reality.