If they think he has liver shunt, a bile acid test may have been done. If it was, what were the results?
Is a regular vet overseeing his case or a specialist?
Neutering can usually be done on liver compromised dogs but for me personally, I think I would wait until test results came in. Since there is a chance that it is a shunt that will need repairing, I'd do the neuter at the same time to avoid anesthesia twice. Even if no surgery is necessary, some specialists like to do liver biopsies (some would rather not) and one could be done during the neuter in that case.
Special precautions are taken in dogs with compromised livers. Quite often the dog is masked down with Isoflurane instead of using any drugs IV. My dog's bile acids were post 47 in the fall and post 106 in the winter and she was spayed with no complications.
What was the kidney problem?
What is your pup eating?
Does he ever get shaky or lethargic?
Does he like to eat?
If a bile acid test was done, had he had any medications (including heartworm, flea and vaccines) about two weeks or less before the test?