I always shake everyone's hand - How can anything erotic come from that??
All the doctors I've ever been to psych plus others have always offered me their hand and looked me in the eye and introduce themselves and if I bring my parents they also shake their hands.
We have been taught there is a place for therapeutic touch but it is a very personal thing left up to the clinician. Although males are warned to be careful when alone with female patients, especially vulnerable ones as they can often misinterpret things and it just takes one accusation to end a career. I think your male T is wise to stay away from touching, especially since you recignise the transference issues - there are just too many potential problems but I find it odd he didn't shake your hand on your first visit. It would seem odd to shake his hand after seeing him for so long.

Does he intentionally stay away from you - by walking a distance ahead/behind you, or acting awkward if you are next to him? That would be weird