I don't see any real reason to mess with a foot pump, since most vacuum cleaners (at least the "cannister" kind) can be hooked up to blow instead of suck, and there are any number of other "blowers" from acquarium pumps on up to industrial style compressors.

I'm not really familiar with the Melodica, but I would expect that when you're not playing a note, the airflow is stopped completely, so your "pump" must not exceed the pressure that the valves can withstand. (Most bellows actuated instruments (accordions etc) need a relief valve to be used when you want to move the bellows without making a noise.)

A bagpipe generally has drone pipes that sound constantly, but more importantly they provide a place for the air to go so you don't make something explode when the melody pauses. I wouldn't expect the normal use of the Melodica to include drones(?).

You might need a pressure regulator or relief valve if you use a constant flow compressor big enough to supply the maximum air flow, and you'll probably want a fairly large reservoir to help with stabilizing the pressure. The little weight/pin assembly from maw's pressure cooker is a simple regulator that should be adequate, with proper sizing. You might have to bore the seat hole in the weight out some to get a little lower than the 10 psi typical for the original design.

Of course, for most mechanical compressors you'll probably want about 100 feet of hose so you can set up the compressor where it won't make too much noise at the place where you're performing; but since you'll want a battery/inverter to run the compressor in "portable mode" you should plan on a sturdy cart so that hauling the whole rig around isn't a problem and the hose won't add much to the rest of the load.

We'll definitely need some good numbers for the flow and pressure requirements for the instrument. (Don't forget to tell us about what kind of music you plan to play, so we can calculate duty cycle requirements for the compressor.)

Or, we could probably suggest something fancy.

John