Maybe you could tether it to the gun and shoot directly instead of trying to fill one from the other?
If you shoot from a rest, you could store the tank in there and attach it through a hose and if you shoot off-hand, maybe you could strap it to your arm (or something).
Come to think of it, somebody should invent a shooting stand / rest with onboard air for tethering. It would make more sense than building 13lb guns like the Hercules.