Two very good points raised - first the respiratory risk of general anesthesia and also the effect on the limb being operated on or not operated on. The respiratory one, I think, is usually the easier to decide on depending on current FVC. If it's good, the risk is relatively small.
I was faced with deciding on a recent foot surgery which would have left me non-weight bearing for 4-6 weeks. I have mild-moderate leg weakness now. Walking is ok on flat surfaces for about a mile, uneven surfaces are pretty treacherous, and stairs are out of the question. So the question was could I risk 4-6 weeks of immobility on my weakest side and HOPE that both the pain would be gone AND I wouldn't gain any additional weakness from immobility - or did I want to deal with whatever pain I was having. Neuro said the odds weren't in my favor (or any of us pALS) of immobilizing any body part for any significant length of time and coming out of it when the same strength you went in with. We all know the adage "use, but don't abuse," but I also try to stick to "a body in motion stays in motion....for as long as my neurons will allow it!"
For me, it was a pain vs. questionable loss of more function issue - I was ready to just deal with the pain, alter my ways, and not risk further weakness from immobilization. In this circumstance described for your husband, it sounds like the immobilization and waiting carries more risk than the surgery itself, which will ideally restore mechanical capability for function and get him back to moving sooner. The downtime for the lungs & diaphragm under anesthesia, even with some mild-moderate drop in FVC, is considerably less than the downtime so far for your husbands shoulder. Like everyone else said, as long as the surgeons and anesthesia staff are prepared for an ALS patient the outcome shouldn't be drastically different than most.
Additionally, there are regional anesthetics that can be used in many shoulder surgeries as opposed to general anesthesia, thus negating much respiratory risk at all.