If all you’re really trying to do is to keep the two layers from separating - it’s not a load-bearing end to end connection - then you can whip stitch the edges together in a minute or two. Get a spool of upholstery thread and a big needle. Go up one edge and back along the other and it will be cat-paw-proof. Draw the stitching tight enough so that there aren’t any loose loops of thread.
Whip stitch tutorial:
