If you are actually interested in gaming out a cat catching a mouse, might I suggest the Cat RPG (
Cat RPG). I think there are others, too. A cat would be extremely offended at your attempt to model them using characteristics like Str and Dex -- cats know they can do anything, and anything they can't do they didn't want to do anyway so there.
If I may be brutally honest, there are two approaches to this kind of problem in RPGs (the problem being stuff that's totally in a different scope or scale than anything the rest of the rules deal with.)
You can
A) Abstract it away by saying "GM Adjudicates", or
B) Meticulously model it in game, find it doesn't work right, add modifiers, scale, rescale, which is really just A dressed up in mechanics.
It's kind of like, the rules never say my guy goes to the bathroom, but I drank all that ale, do I need to roll to see if he explodes? No system models everything.