I've found that cross-cut thin paper shreds are best in the coop, and if I put in enough then there's no smell even first thing in the morning when I open the door.
All my paper shredders are cross-cut. I wonder how micro shredder paper shreds would do in the coop?
I bought my cross-cut paper shredders at the Thrift Store for less than $5 each. I have yet to see a micro-cut shredder for sale there. I'd buy one for sure just to try it out.
I did not have enough paper shreds in the coop this summer. And when I mean I was starting to smell the coop, it was not overpowering or anything. But my highly sensitive nose picks up on the slightest indication of an ammonia smell and I need to add more fresh paper shreds. Usually, I stay ahead of the game and have only needed to clean out the coop twice a year. But, as I said, I had to do some maintenance on the vinyl floor covering in the coop so I decided just to take out the soiled paper shreds under the roosting bar, fix the linoleum, and put in fresh shreds. Not a full cleaning of about 10 muck buckets full of liter for the entire coop, just 2 muck buckets full from the litter directly below the roosting bar. I don't do my full fall cleaning until sometime in late October, right before we can expect snowfall.
On the floor of the run, something more substantial is better - shredded twigs etc and straight-cut heavy duty paper or thin card worked well last winter.
My paper shreds include not only office paper, mail, and newspapers, but also all the light cardboard boxes from cereal and other food products from the grocery store. The light cardboard shreds are more substantial than regular shredded paper. I have also shredded heavier packing cardboard boxes, and it works fine, but I find that that cutting up the cardboard boxes into strips for my shredders is generally not worth the effort when I have so much other paper that is much easier to shred.
I don't want to burn out my ~10-12-page max capacity shredders running heavy cardboard through them, so I have been cutting down the heavy cardboard into strips that go into the "credit card" slot of the shredder - which is usually 2-3 inches right in the middle of the shredder.
I once overloaded an older shredder with heavy stock. The teeth were fine on the shredder, but the plastic gears that turns those teeth broke under the pressure. Since then, I just feel it's better to keep the paper input under the max capacity rating of the machine.
For awhile, I was also mixing other litter in the coop along with the paper shreds, such as dried leaves and wood chips. I am all for using whatever free litter resources you can find that work for you. I really only use straight paper shreds now. I used up all my wood chips over a year ago, and although the dried leaves work just fine, they were also very dusty.
In spring/early summer I scraped out the loose stuff from the floor of the run and put it in trenches on my allotment plot, ready for planting climbing beans. I was delighted yesterday to be complimented, by a retired market gardener, on how well the beans have done! I gave due credit to the chickens

I compost all my coop litter. The paper shreds compost much faster than the wood chips I used to use as litter in the coop. Paper shreds also seem to compost faster than dried leaves, but the chickens can do an excellent job of ripping up dried leaves to bits and pieces as well.
I turned my entire chicken run into a chicken run composting system, so when I dump out my old paper shreds coop litter, I cover it up with a load of grass clippings from mowing the lawn. The green grass clippings prevent the paper shreds from blowing all over the yard while at the same time sped up the composting process. I try to keep a nice carbon to nitrogen ratio in my chicken run compost litter. All my organic material from around the house gets tossed into the chicken run. All my grass clippings, weeds from the garden, and all the fall leaves get tossed into the mix. It's all organic as I do not use any chemical sprays on my property.
I see my paper shreds composting down to useable material in about 3 months, but I let it sit at least 6 months so the chicken manure in the litter has a longer time to age and cool down. I have so much compost in my chicken run now that I am only harvesting compost that I started 2 years ago. I sift out the compost and add it to my raised bed gardens. It works great and my plants just exploded this year. Very, very, very happy with the results using my chicken run compost. I don't use any other chemical fertilizers.