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Not yet a PCV, but as a fellow uke-enthusiast, this sounds awesome!
Perhaps you can use age limits to control how many kids can join. Like, 10 years old and up (IDK what ages you have in your classes, but just as an example) can join the club. You may want to also be a bit strict about attendance. That way kids can't just join for the instrument and then quit 2 weeks later and you never get their uke back. Maybe they have to attend for a certain number of weeks before they can take their instrument home and/or if they miss a certain number of meetings, they are bumped out? It sounds kind of harsh, but you have to protect the instruments and make sure that the kids who are there want to be there and are willing to do the work. I would also definitely have them sign some sort of contract/pledge detailing how to take care of the instrument before they are allowed to take them home.
Oh, and teaching them TAB, instead of how to read music, may be a bit simpler. You can get chord posters for pretty cheap and then the whole group can see the fingering.