It may be that a lot of the wires are direct runs to the devices they control or it may be that the entire panel has connectors that allow it to be disconnected and removed.
My first reaction to your question is that if you are asking if the job is over your head, it may very well be
Now if the wires are in good shape other than the chewed sections, you may e able to undo one end and slip a piece of heat shrink tubing over it and shrink it. To do so, you may need to cut off the end terminal connector and after heat shrink, reinstall a new terminal.
If the chewed spots are small, you may be able to cut the bare spots and reattach using butt crimp connectors.
Wrapping the bare spots with tape will not hold up.
Be aware that there may be dozens of color combinations and it won't be practical to rewire using the original colors ( which tell you what the device is in most cases) Make sure you tag and label everything and take a ton of pictures.
Finally, if you are going to crimp on new connectors, use good quality heat shrink connectors and a good quality crimper. That toll might cost $50 but is a necessity. Buy extra connectors and practice first on spare wire.
Finally,, just take your time and have fun.