They use a slip collar or noose.
It isn't going to hurt UNLESS the dog pulls.
Then it is just like having a collar attached to a leash.
The only way I would allow one of those to be used at the groomers is if they agreed to put it around his chest, not his neck.
I don't want to scare you but please also make sure they do not leave him even for a minute because, with that around the neck, I think I've heard of dogs jumping off the table and getting strangled.
I just groom myself and don't have to worry about it.