What about using the battery packs used in cordless drills / power tools like the De Walt 18V packs or Ryobi One systems?
Find a damaged drill and cut the base off to re use the socet, or just solder direct to the terminals and use a charge module to charge it up. You can buy the batteries separately too.
They are lightweight, have a good charge storage and are pretty rugged, so put up with a bit of pounding.