A wooden cat is a toy that can be made using the Crafting skill, after partial completion of the questThe Great Brain Robbery. During the quest, 10 of them are needed to fool Rufus the meat trader into thinking they're real cats. After speaking to Rufus and watching a cutscene, you will be granted the ability to make wooden cats.
They can be made on the crafting table in your house with a regular wooden plank and one piece of fur (werewolf fur, bear fur or grey wolf fur) gaining you 15 Crafting experience. Attempting to use any fur from a Hunter creature will result in the message: "The only fur you have is too nice to waste on these cats. You should try something else."
If both fur and grey wolf fur are in the inventory when attempting to craft this item, the fur will be consumed before the grey wolf fur, even if the grey wolf fur is closer to the top left of a player's inventory. If you want to ensure the grey wolf fur is consumed, you must put the plain fur in your bank or drop it on the ground before attempting to make this item.