When levering, I like the tire iron over the screwdriver as it has a larger flatter surface to distribute the levering forces.
If you think about it, you don't want to apply force to the perimeter of the live pad, it will cock in its surroundings and bind a bit. Put the tip of the lever in the center of the pad, shielded with a sliver of clean sheet metal or cardboard so that you get a straight push into the caliper.
If the caliper/pad area is dirty, might be the chance to loosen the 2 bolts and separate the caliper as suggested, remove the live pad and clean around it.
But quick and dirty, the lever should work.