Despite the conflicting titles, Viviane Schwarz's There Are Cats in This Book and There Are No Cats in This Book are both loaded with friendly, playful kitties with which the reader can actually interact. You can throw them their ball of yarn, play hide-and-seek, and even have a pillow fight or help them pack for vacation. These are no ordinary cats.
Although the books might seem to be meant for interacting directly with a single reader or listener who is sitting right there, able to touch the pages & play one-on-one with the cats, both titles still do work very well in a storytime setting, with the adult reader getting "coached" by the children present to act as their surrogate.
Once you've met the cats & played with them, you may want to extend the feline fun beyond the pages of the books. For the crafty type, there are patterns for knit versions of the cats. For the rest of us, though, you could just print out these scissors-ready kitties that are ready to stick anywhere & everywhere!
Don't hesitate to pick up the cats from There Are Cats in This Book and There Are No Cats in This Book. You'll have a lot of fun, and I promise you: you will not have to use a lint brush after you put them back down. Check them out!