Unfortunately this is very common in Yorkies.
Why is he still at the vet if he isn't doing anything for him?
While it does sound like a shunt, without blood work the vet can't possibly know...
This surgery is usually done at a university. The U of Tenn. is the place of choice. they use an ameroid constrictor to slowly close the shunt while some other surgeons use the cellophane band. The constrictor seems to be preferred.
What food does the vet have your pup on now and has he been started on supplements.
the U of Tenn. has a page dedicated to this disease. It is easily Googleable.
It is possible that it is Microvascular Dysplasia (small shunting throughout the liver) and in that case, surgery cannot be done. It is managed by diet and supplements.