OMG He’s adorable and looks a lot like our little trouble maker, Moki. When I was using my Rigid Heddle I made a quilted piece that velcroed over my project. It did not stop them from laying on it unless I hinged it to vertical when not using it. That is not useful to you, though. My cats hang out with me in my studio often, though so far haven gotten on the loom. Chloë loves to hide in the paper roll when it hangs down, and roll around on my wonderful rug.
I’m thinking, Kathleen, that a cover might not stop him, though. He’ll probably find a way to climb up under it, making it a great little hideout!