I've used paper from a shredder with some success. It does tend to blow around quite a bit if you have the diamond cut type of shredder that creates about 1-1/2" pieces. If you have the type that just makes long strips, that works better with less blowing into the yard. The small stuff ends up making the back yard look like a ticker tape parade on windy days. What I have found to work is mixing the paper bedding with shavings and that works a bit better. Also know that when it gets wet, it stays wet longer than other bedding and mats down. I happen to live in a really dry climate (usually! funny rainy weather lately...) so the paper wasn't a problem when we were brooding chicks a few (dry) months ago. But since putting the girls in the coop I have learned to mix the paper with other bedding...
Also watch your birds to be sure they aren't eating the paper. I've actually watched some of mine swallow it, worry for days about an inpacted crop, and they still seem fine. But I would keep a close eye on it. They seem to be attracted to some coplors of ink or paper more than others. And check with your newspaper that you are using if they use a non-toxic (usually soy) ink.