I don't know what kind of shield/cover you can use because the cat gets hot. It would be bad to direct this heat back towards the chassis. I thought of something that might be adaptable, tho.

In Germany they have these weasels that enjoy a crawl around inside engine compartments. The rodent leaves his scent all over everything and eventually another one comes and tries to destroy trace of previous weasel, chewing up all manner of hoses and wires.

One of the solutions they have to counter this is to install electrified rods, grids and plates that mount to the undercarriage of the vehicle. Sort of like an electric fence. Some cars even come so-equipped from the car factory.

Here is an example of an add on kit.



And here is such a rodent.


Edit: Since I mentioned an electric fence, I thought about a cattle fence. Why not just coil barbed wire around the exhaust?