Aw poor little guy I assume its his molar (back) teeth?
I don't see why he couldn't be neutered and have his teeth done at the same time- I've had this done before with my rabbits.
Also, looking to the future, could you find a vet who will do teeth without a GA? Mine does- the benefit is that it does not have the long term effects of a GA and the often long recovery period. Sometimes they give them a whiff of gas to make them calmer whilst its done.
Obviously I don't know your bunns history, but it sounds wrong to me for him to be PTS if its just his teeth- I would find a new vet if I were you!