Is there anything wrong with just keeping two different scores and show the mouse and cat scores for each player? A player's skill as a cat would be reflected simplest by the number of times he catches the mouse. If one player is faster than another at catching a mouse, his score will naturally be higher. If a player is able to avoid being eaten when vulnerable, whatever penalty he experiences for being eaten won't get in the way when the mouse is vulnerable again and the score will likely reflect that.
While it is true that I could keep the scoring like it is, I think it will be more interesting for the cats to get some points while chasing the mouse, instead of only getting them when the mouse is caught. Plus, this is what's going to make the difference between a great and an excellent cat player.
I could also drop the secondary scoring system and reward items based on skill. This is a brainstorm kind of question, I'm just trying to see what possibilities we can come up with and choose the best one.