I watched some YouTube videos last night on using cardboard for chickens. One lady said she switched over to using bagged cardboard bedding which was sold at their local farm store as horse bedding. It was less expensive than straw, which was what she had been using. She preferred using the cardboard bedding for lots of the reasons I have also mentioned. Compared to straw, the cardboard was more absorbent and no dust. I would say that applies to any paper shreds in general, not just cardboard bedding.
Not that it makes a big difference for coop litter, but her store-bought bagged cardboard horse bedding was in pretty big chunks compared to the cardboard shreds I get from my paper shredder.
Another video had a guy that was shredding cardboard boxes in his home paper shredder, like I do, and he was dumping the cardboard shreds into the next boxes as well as the coop floor for litter. So, I think the heavier cardboard shreds might work out OK in the nest boxes and not stick to the eggs like the paper shreds I normally make.
I watched one video and the guy was recommending getting a paper shredder rated for 24 sheets. He spent about $150.00, 3 years ago, for his shredder. He was able to shred up cardboard strips a full 8 inches wide with no problem in his shredder. However, he never thought to mention that you can use a less heavy duty paper shredder, like my 12 sheet shredder, if you just cut the cardboard into thinner 2-3 inch strips and feed them down the middle of the machine that is designated for credit cards. That works just fine on my $4.00 Thrift Store used paper shredder. So, you don't have to spend a lot of money on a heavy duty shredder to get good cardboard shreds. You just have to cut thinner strips to begin with.
There was one comment that I found I agreed with 100%. The guy was using a utility razor knife to cut his cardboard. But he mentioned that using the utility knife was a pretty dangerous method of cutting the cardboard and if you slipped, you could cut your fingers pretty bad. He said he was going to get one of those power cutters from Harbor Freight - like I just purchased recently - because they were so much safer, and they had great reviews.
The normal price for the HF power cutter is $40.00, but it goes on sale for $25.00 every few months. Like I said, I got my HF power cutter on sale, I had additional HF cash rewards checks that I needed to use, and I also got a free gift the weekend I bought my power cutter. So, I really lucked into a great deal.
These power cutters are made by many companies, and as far as I can tell, they appear to be the same Chinese model with just different colors or company branding on them. Even the replaceable blades seem to be interchangeable between the brands.
Even if you ended up paying full retail price of $40.00 for this HF power cutter, or other brand, it would still be a lot cheaper for you to cut up your cardboard into 2-3 inch wide strips to feed into your existing, or less expensive, paper shredder than buying a new 24 sheet paper shredder for $190.00.