At present I on;y know of three options: unmodded (spawns 5 Large Dogs, 5 Small Dogs and 5 Cats), No Stray Respawn (which disables spawning altogether), or dickhurt's hypercomplicated "Pet Modifications", which affects way too many other things besides number of strays.

So, how would one go about modifying just the number and kind of strays? (Specifically, I would like more cats and fewer dogs.) Recommendations?

Are you asking for help with BHAV modding, or is this a WCIF?

Modding discussion would probably be a better place for this:
https://modthesims.info/f/8/