Maybe a small compact bicycle pump? That would work if you could get one small enough.For what you're doing with it, the inner tube is probably indestructible.
I wonder... I'm not sure what they're called, the inflator bulbs on a blood pressure cuff... could one of those be hooked up to an inner tube, so you can inflate/deflate it? Maybe deflate it to pack it smaller, or to adjust inflation for comfort.