I haven't had a problem with any of my dogs (not yorkies) being anesthetized...but yes, there is always a risk, big OR small. If you are worried, have the bloodwork done to be sure he is healthy going into the surgery.
I will second it being important to have their teeth cleaned, and keep them in good shape. I have an older dog in residence (he does not belong to me, but retired here from the breeder) who came to live with me at just over 8 years of age. His teeth were a mess when he came to me. They have improved greatly without vet intervention, but he was recently diagnosed with advanced oral cancer. Though we can never say for sure whether having his teeth properly looked after all his life would have helped, I really wonder if it would have.
That dog's daughter, who I've owned since she was 8 weeks (and is now going on 7 years
!!), she had to go in and have a tooth removed a year ago due to a slab fracture. The tech said they would do a cleaning as well since she was under (and it was 'dental month'). Ok....when I picked her up, they said they were very impressed with the condition of her teeth, that at 5 1/2 years, they didn't have to do a cleaning at all! I keep lots of things around for my dogs to chew on (except rawhides because I have 'power chewers'), but the downside to that is they sometimes break teeth
knuckle bones, tartar busters (patellas), antlers, nylabones, there is a never ending assortment lying around for them to get a hold of at any time.
Feeding good quality food is also important in keeping teeth in good condition.
~kathryn