How big is the cat, and what type? Before anything else, I would leave it for awhile to see if the fish manages to spit it out on its own, as long as it appears to not be excessively agitated.
If it doesn't cough it up, a long pair of forceps should allow you to pull it back out through the mouth. You can make a wire "gag" to hold the mouth open so that you can see what you are doing and reach in. If the fish is big enough, you can use a jaw-spreader, sold in fishing tackle stores for just this purpose, i.e. removing hooks and lures that have been completely taken within the mouth.
This is nerve-wracking, especially if it's your first time, but it is surprisingly easy to do. If the object seems jammed up awkwardly then you could even reach it with wire-cutting pliers and snip it into pieces for easier removal. Hold the fish in a wet towel, be careful of the pectoral and dorsal spines, and just work quickly and smoothly.
Good luck!