Left unchecked a damaged handpiece cable can destroy your control box and/or cause permanent damages to the motor of the handpiece. Both of these problems will end up costing far more than just replacing the cable.
Cables wear out, they get cut with sharp objects, melted with hot objects and stretched and twisted in all types of directions. Don't try to "deal with it" by holding the cable at some awkward angle just to get the handpiece to operate. Also, trying to repair the cable is a bad idea because 99% of the time it doesn't get fixed properly. Just replace it and save yourself the headache of having to spend $300 - $400 or more to replace a damaged circuit board.
If you've got a short in your Schick or Microstar handpiece cable the best thing you can do is order a replacement.