John: I have often thought about using a foot pump with the squeeze type faucets also. It's hard to squeeze the faucet, pump the pump and hold your cup with only two hands. I found this:
Mini Foot Pump - A Bikers Dream
My only concern is with the cleanliness of the air it would provide. I doubt it has food grade "O" rings and lubricant inside. Maybe you could convert it? The hose assembly could be swapped out with 5/16 beverege tubing and fittings, but I'm not sure about the innards. Good luck!