re; removing the stuck piston, and pad. If you're replacing the pad, I'd try to remove it first, with wide open pliars, or lever of somekind. About 80% of the time you can stick an air hose, as proposed, to the brake line inlet port and blow the piston out. If its going to come that way, it will come flying out, so aim it into a towle or outside or something and keep your face away.
For the ones stuck even harder, remove the end from the hose of a pump style grease gun. Thred it into the MC, the threads aren't the same but you can catch a few threads and that's all it takes. Pump away, the piston will move a slight amount with each pump, after filling wiith grease. But surprise it will come out this way. Then clean up the grease.