What about supplying power to the drill through a relay that is held ON by the Arduino and goes OFF when the contact with the wire is detected.
I suspect your bigger problem will be reliably detecting the contact quickly enough to avoid damage. I would be tempted to try a much higher contact voltage - 30v or 50v - as high as you can without risk of personal injury. Obviously you can't feed that high voltage direct to the Arduino pins so you will need an intermediate device or at least a couple of resistors to make a voltage divider.
...R