You could glue the cork, couldn't you? A woman we know refurbished her old custom kitchen with cork - she put it on the kitchen cabinets and fridge. It really looks nice.
Yup, we could just glue it on. But Gary pointed out why cork (even though he loves it) would be a bad idea - the kitties will ruin the parts they can reach. He's right - it'll get ripped to shreds.
Good point, since you have several cats and at least one would probably love it. We've got cork wallpaper in the downstairs hall, and haven't had a problem, but have got sisal scratching boards on one wall in the logical scratching place (beside the door to the cellar).
There are also those self-stick mirror tiles that might work.