Try and soak the parts you can not see with penetrating fluid, careful not to get any into your pad/disc contact sweep area.
Using emery cloth, bring the exposed parts of the pins back to bare metal.
With a shortened pin punch (just thinner than the pins) tap the pins from the back. Many small taps are better than a few mighty blows, to minimise damage mushrooming of the pins. When they start to move, work them in and out, keep applying penetrant.
This is a lot easier done on a ramp, 'cause the access and space to work is limited. Better would be to undo the two 17mm caliper bolts to get clear access
Being as young as a Hawk, surly they can't be too bad! Good luck.