What to do with a mid-stage Alzheimer's patient who won't follow doctor's orders?

The problem may be the "shortly after waking". If he's not a morning person, he definitely may not want to greet the morning with a nebulizer. As an asthmatic who has lived that "twice a day" medication schedule for decades, I can tell you that an hour or so one way or the other seldom makes much of a difference. You might get a little more cooperation if you let your husband wake up and enjoy his coffee before bringing out the nebulizer for his "breathing treatment". I recommend using a pleasant/excited tone to announce its time for the treatment, like we get to go fishing today! Sometimes talking about the benefits of the medication during the treatment works too; "I'm so glad the doctor found this medicine and you don't cough so much through the day anymore". I'm not sure the dementia patient responses to your actual words or more to the fact you talk to them in a pleasant voice but I have found my LO reflects my mood or attitude. If I expect problems and communicate that with voice or actions, I am more likely to get the uncooperative side of my LO.

For more suggestions, have a look at

https://www.aafa.org/asthma.aspx

This is the website of the Asthma and Allergy Foundation of America, which seems to have a lot of useful information about advice, resources and support groups.

I would also recommend playing his favorite songs (only) when he is getting treatments. Doing his favorite activities afterward. Putting on his favorite TV show. Small rewards so he associates the treatment positively.

Listen to the physician - as long as your husband is of sound mind he can make up his own mind whether to be in discomfort or use the drugs he knows work. It really isn't your problem, you are happy to assist if he wants it, if not be happy for him to make the decision on when he will medicate.

Ahmijoy is right, not much you can do without causing stress on both of you. Do the best you can. Can you ask the doctor about palliative care ? Maybe he can be evaluated and then someone can come to your home and try to give him the treatment? treats are always a good standby. Most of the time they work.
your husband probably doesn't understand and he wants more control and probably feels he is losing control. It may feel like snorkeling. Sometimes people get a little apprehensive having to breathe in n out of a snorkel until they get used to it. In any case, he amy just feel uncomfortable using it. Try a shorter treatment if you can. Just a couple of breaths into the "snorkel",and build your way up to the full treatment. You may want to play Nemo, the movie since there is a scene about a mask and snorkel. It's a fun movie if you haven't seen it. I'm trying to think outside the box.

The doctor is, unfortunately, right. You can’t wrestle him to the ground and shove the nebulizer mouthpiece into his mouth. Does the medication make him feel odd? I know my husband didn’t like the feeling the meds gave him when he used one.

You can try bribery if that would work with your husband. Promise him his favorite breakfast if he endures the treatment.