Actually....I kind of agree with your vet. Anesthetic for a dental cleaning would most likely be too much strain on him. The best you can do is buy a special dog-toothpaste and brush, and brush his teeth very gently.
However it is possible the bad breath comes from deeper down. It may be his organs are not functioning very well....kidneys/liver etc.
Has he started eating anything again? If he stops eating or throws up what he eats, then that could be a sign of kidney failure, and that is very unpleasant for a dog.
Drinking water and keeping it down is a good sign. To give him a little extra energy especially while he isn't eating you could dissolve a little honey in the water. He might like that and it might perk him up a bit.
I hate to say this....and I might be wrong...but he could be drawing gradually to the end of his life. Just keep him as comfortable and as happy as possible. Don't worry about the scale and polish. But if he is in actual pain from bad teeth, then an antibiotic and some painkillers might help him a lot.
I am all for a gentle but sensible and loving approach to old age in dogs. Some vets don't quite understand how to handle old age.... Some treatments do not suit an old dog.