Sounds like you got the handles with them. You can replace the wood without taking the metal off the blocks, and you might consider that if you have plenty of handles and some of the screws are really stuck.
Soaking in penetrating oil never hurts, and a light application of heat often helps, but drilling is an absolute last resort. The best way to take out stuck screws is with a drill press. Unplug the press and chuck a bit shaft with a rachet over it. Clamp the blocks in a vise, apply downward pressure with the drill press, and turn with the ratchet. Bit can't slip and the screw will either come out or bust off. I have very rarely broken one off, but that's the time to consider drilling.
