I hope my experience helps your husband. My 3 year old just had her tonsils & adenoids taken out 2 weeks ago. She was born with enlarged tonsils and has been a noisy sleeper since the day she was born. She rarely gets sick and never had tonsillitis so I didn't see the reason why she should have surgery. Even after two pediatricians and two pediatric ENT specialists suggested she have surgery, I was still against it.
Although it is a routine procedure, it is different when it is your own child and I didn't want her to go through it if it wasn't necessary (of course my own traumatic experience as a child didn't help.) I finally accepted the inevitable, but I just wanted to wait until after her 3rd birthday. The surgery was textbook and my daughter did great and recovered much more quickly that I expected. Kids are so resilient!
The doctor told us that when she was on the operating table the tonsils completely obstucted her airway which scared me! Then I wondered why I let my fear delay something that was so obviously necessary.
So, my advice is to talk to your ex, find out what he is thinking and go from there. It is probably irrational fear keeping him from saying no. I agree with another post that he should also speak to the specialist so he can ask questions. Although I believe that tonsils are there for a reason - to fight infections, sometimes surgery is necessary.
Good luck and I hope it all works out!