I understand how your husband feels, as someone whose guitar/bass is never far from their hands. Unfortunately, I don't think there are many good solutions. I've had to fly with my guitar a few times and it makes me incredibly anxious. Airlines are notorious for damaging musical instruments. The best you can do to protect your instrument is buy a very heavy duty case (like a good Gator hardshell case) and request to gate check it. Sometimes they will let you put it in the little locker/cupboard they have on bigger planes but you won't know if they have space until you're actually boarding. I know they also make smaller travel sized guitars but I don't know if they're small enough to be a carry on. You could, if you are desperate, consider something really small like a ukulele.
Renting could be an option, depending on where you are going. Or if he just wants some time to practice every day he can walk in to any guitar shop (we have many here on Denmark Street) and just start playing. You don't even have to pretend like you want to buy something, many guitar shops will just let you play!
Good luck and hope you are able to find a solution.