One of our dogs loves to shred cardboard and egg cartons, like you describe. He also really likes toys like this, and will spend time carefully rooting out the smaller toys from inside. As long as we don't leave the small toys out for too long, he seems content to play with them as they are designed and not destroy them.
https://www.amazon.com/Squirrel-Interactive-Outward-Hound-Ginormous/dp/B005VS9WO6