The hydraulic method is the safest and best. You can use the the master cylinder, with the caliper dismounted and pads removed start pumping. The outer piston, usually, wants to come right out and must be restrained so that the inner piston feels all the pressure. You can do this with hose clamp and metal stock; the possibilities, however, are many. Once the outer piston is restrained the inner should come right out.
Once the caliper body is bare and clean inspect the seal grooves for oxidation; a Dremel with a wire brush works well to clean these grooves, but wear eye and face protection because these wire brushes don't last long and trow off their bristles with significant velocity.
Best.