I don't know if either of you are seriously contemplating buying an accordion fare, but ... I believe I've read anecdotal reports that even this "didn't fly" if you'll excuse the expression, when the cabin crew refused to go along with it. They're responsible for getting a planeload of people safely from point A to point B, and if some flight attendant gets spooked by the idea of a poorly secured, apparently heavy object in one of the seats, they can say "no" and everyone will back them up. (I've never heard of anyone trying it with an accordion, this was likely a tuba.)
In the US we have a law, or rather an act of Congress, that establishes some standards in support of musical instruments. Not sure how it would apply to a flight originating abroad. But they gave the responsible agency two years to implement, and I'm sure they'll take every minute of that, so it's irrelevant anyway. This was necessary mainly because of the capricious way the airlines have handled the matter when left to their own devices, and I suppose that in the interim there's no reason to expect any better of them. So ... good luck! Really it shouldn't be too bad - anecdotally anyway, most travel stories I've heard have been successful. (By the way, American Federation of Musicians union gets substantial credit for the legislation.)
If you carry an accordion on board, I suppose the main risk is that you'll be obliged to surrender it to a gate check, where someone carries it off to be stuffed in the hold. That's often thought to be relatively safe, but it depends. My bari sax got smashed that way. The flight crew carries most of the stuff - baby strollers, etc. - down from the cabin on this mobile staircase, but that thing also has a little slide, and if your item looks heavy and unmanageable, it may go down via the slide, which will likely be worse than anything that would have happened if you'd just checked it as normal baggage.
heard that someone once checked a tuba, on a flight to China, simply wrapped in bubble wrap - no case - and it arrived without a mark. I think that may have been a rather shrewd strategy, really, compared to the usual notion of a huge, unmanageable case that gives the appearance of being very robust - an appearance only, because it's very hard to pack a delicate item inside a case in a way that really protects it. Dropped from several feet, a tuba - or an accordion - will essentially damage itself inside the case. Despite their reputation, baggage handlers just want to get through the day and don't often really have any ambition to wreck your stuff, so if it looks a little fragile they may take it easy.