I don't think Gil sees himself as a "big guy," but I do see him as the sort to not want to kill the cat straight-out. Even so, I'd buy it more if catguy were Nick.
I don't see Catherine taking possible evidence from a crime scene, even if they were just the cat's things.
Al the autopsy guy has a cat -- a Siamese that had kittens -- perhaps he could do insight on this.
A cat who puts his toys away? It's like the time when Adrian Monk found that parrot that had gotten depressed and spent all its time cleaning its cage.