I just uploaded this little mechanical kitty to Thingiverse, and I think you should make a version for yourself. After a few trials with some cheap 1/4″ plywood, I ended up splurging on pressboard made specifically for laser cutting. The first cat I cut from the cheap ply ended up burning so much it was hard to get something functional out at the end. I blame the adhesive used to laminate the sheets. I think I might try and source some thin ply made with a natural wood glue. In the meantime, Laserbits makes some excellent laser specific stuff.