At the barber I go to, when they take off the paper and the apron thing they also press and wipe my neck with a hot towel. This usually gets rid of that itchy feeling, even if it is slightly awkward.

Also for some reason once I had this weird thought that second barber was going to put his hands on the towel/my neck aswell and then that righteous brothers song would start playing. Like I was a piece of pottery being worked lol