If you hang the bike, then it won't matter. Just put in good tubes and pump up the tires before hanging it, and as the pressure drops, even 1 PSI should be enough to keep them round.
Many tire shops fill industrial tires with a solid rubber stuff. You can ask around locally. Tell them you have some bike wheels/tires to bring in and ask them if they'll fill 'em up when they do the next batch. Do it on their schedule, and it shouldn't cost much.