This idea came to me only today as I filled my second bag of shredded materials that this could easily be used to cover the bottom of a rabbit cage, a free alternative to expensive bedding. I generally choose the recycled paper option anyway. Add a little baking soda to help absorb the odor and you are set!
As for the environmental impact of such a change in habit, I would qualify it as a "lesser of two evils" option.
What do you do with your shreddings?