I'd be fairly careful about experimenting with USB power supplies. USB power is essentially 5v, it is meant to be between 4.75 and 5.25v (ie ±5%). Whilst going below this probably wouldn't do any permanent harm, exceeding it could quite easily fry delicate electronics.
The problem is going to be with making a power regulator circuit which can take a substantial variation in voltage and efficiently convert this to 5v.
Simplistically you could just rectify and smooth it, and bung it into a suitable zener, although this would be wasteful, since you are just going to be dumping the excess power as heat. It should be possible to build a small switch mode supply, but I suspect it would be relatively inefficient.
I think I'd rely on a battery pack, since they seem to be fairly easily available. A very quick Google found
this Li-Ion power pack. I'm sure there are cheaper devices available.