That looks totally repairable to me, especially if only as a temporary fix. If you are not comfortable doing it Im sure a local mechanic or stereo installer could do a excellent job of fixing it....its only 3 wires and the socket side of the coil can be removed and reinserted.
Cats kill anything they can, including things that aren't pests/nuisance. Domestic cats are the second leading cause to bird population decline, right behind global warming.
Get a glue trap instead, or google 'water bucket mouse trap'.
Agreed, the only reasonable exception to that rule is if you put a harness on them and take them for a walk, so you're really just supervising them while they're outdoors.
I now return you to the thread already in progress...
I agree with @Kodiack : Someone good with wiring/a professional could likely repair that for you if you can't find the part.