He doesn't have any choice. If they told him to get it, he has to get it. A lot of the military is getting the mist now. At some commands, they only let pregnant women get the shot. The mist is a lot better for your husband than the shot they'd give him. The mist might cause a mild case of the flu, but at least it doesn't have any thimerosal in it, which IMO can do a lot more damage than the attenuated flu virus! I wouldn't worry too much about it. We got sick after DH's command got misted last year, but it wasn't bad at all. I don't want us to get sick, but I'd rather risk us getting a very minor illness than my husband getting an extra dose of thimerosal. I'd prefer neither, of course, but if I had to choose, I'd take the risk associated with the live vaccine. Sure thimerosal doesn't present any risk to me and my daughter, but they already get sooo many vaccines with soooo many preservatives and nasties that I don't want my DH getting an additional dose of mercury when he doesn't have to.
I'm assuming you guys are at a small command, so it might be hard to get out of it by making friends with someone. At larger commands, it's sometimes easily avoided just by telling the person administering the shot that you don't want it. They don't personally care and will usually be fine with that. Since that's not an option for you and it sounds like this year they're pissed about him fighting back (never, ever, ever a good idea when it comes to legal, FDA approved, tested vaccines, btw - it just makes them mad and it doesn't help you any) then he'll probably just have to go get the mist this year. Next year, however, he should seek out a civilian doctor who has the thimerosal-free vaccine in stock and pay for it out of pocket as soon as it becomes available. Then when it's time for the flu vaccine at work, he can tell them he already got it and provide his bill and record from the doctor who administered it. It's very, very, very unlikely that they're going to care or make him get another vax (although not impossible, of course). They're just mad this year because he's arguing with them. His CO probably also doesn't get to decide what flu vax he's supposed to get - the military probably told the CO what they're going to pay for and that's that - so demanding that the CO care about the science and get him another vax is probably pointless, since it's probably not up to her/him anyway.