Hello Winterjay. A non-toxic glue should not bother your pets. I use gorilla glue on my DIY projects and it's been fine. All of my fluffs like cereal and biscuit boxes and LOVE chewing them up. Gerbils are especially fond of this and will turn them into the softest fluff you can imagine. Go ahead, they'll have a great time with it and you will enjoy watching the fun!
I stay away from newspaper and magazines because of the ink in them.