I'm not sure what Jim uses for finish on his speakers, but I wouldn't recommend anything with adhesive. Sometimes the interaction between finish and adhesive is not evident immediately. Could be nothing or possibly discoloration, but I've seen adhesives soften finishes to the point of failure. I'm sure it's explainable chemically, but I doubt you want to involve your new speakers in an experiment.
Seems like something to discourage the cats would be a better plan. Perhaps a piece of felt that slides when they jump on it. But then I can see them grabbing and clawing in the fall, potentially snagging grill cloth or even scratching finish depending on their tenacity. I have used odor type repellants, but never indoors. Perhaps a visual foil like a tented piece of paper or a piece of pottery. The few times I've dealt with cats, it seems that once they find "their spot", they want to return, so discouraging from the get-go likely a good idea.
No first hand experiences in our house though. No pets, and the grandkids know if they touch Grandpa's audio stuff, they'll lose a finger...
If the finish is actually automotive urethane, the protective film is unlikely to damage, but if it's lacquer of some other solvent based finish intended for furniture or cabinets, I'd be a little wary. I doubt he uses conversion varnish, but if so, that's a really tough finish, more so than catalyzed lacquer.