How to fix a warped parquet floor?
You can try whatever to the board that is warped.  If it works great, if it doesn't you are back to square one.  Mineral oil plus dumbbell may work, but it is a factor of the amount of space that is there below the wood.  I seriously doubt you are going to condense the water logged wood.  So your objective would just be to have the wood flat on the surface.

Your other option if the wood is just bulging is to sand it down.  Often for small areas this has a decent chance of working.

If you want your hardwood floor to be a bit more resistant to water than you need to hit it with a few coats of polyurethane.  With cats this seems like a no brainer to me since if they piss it will soak into the floor (and possibly smell like cat pee forever).