I don't know about the influence from the magnetism of the screw driver, but I do doubt whether you will be able to get accurate compass readings in proximity to steel tools. Generally I have found that my various steel tools tend to bias my compass readings when they are within 6" or so of the compass. Keeping the compass farther away from the tools is probably better. You might want to relocate your compass, or at least attach it to the key ring with a detachable connection.

Good luck,

John