I agree a trip to a good vet would be excellent.
Maybe it's just me and I look after human little ones, not furry ones but every time someone raises the spectre of anesthesia as a problem, I cannot help but wonder about other options - like we do for tiny babies , pregnant moms, people with compromised respiartory systems like me - there are ways to have surgery without full blown anestehesia AND there are some newer meds now that are almost like ans. I am thinking epidurals as well - I had a laparoscopic cholycystectomy - gall bladder removal -with just an epidural and it worked very well. Surely vet medicine has improved as fast as human surgery? Ask for a vet who can do some of these newer (in the vet world) procedures - and I know they must because we have sold some of our equipment to vet clinics.
Good luck and thank you for saving this doggie!