No need to fear chemicals, your lawn is already being sprayed withdihydrogen monoxide on a regular basis.
You’re funny. I actually pulled that trick on my mom and stepfather last week. 
I built my garden on horse poop. The soil started out horrible, full of clay, but it is now wonderful. It takes a few years, though.
When my daughter rode we drove our truck out to the barn and filled up plastic bags. They have to pay to get it carted away, so they will probably be thrilled if you ask. I solved the composting problem by digging into the middle of the pile where the poop is more mature, and also by adding it the fall before I planted. Never had a problem.
It’s funny, but it also makes a point. Chemicals are everywhere, in labs and in nature. Thinking anything that’s a chemical is bad is just plain wrong. The chemicals in fertilizers and other treatments are things already present in healthy soil.
Oh, about those trees/shade - a good arborist can prune back the old/dead/crossed/unnecessary branches which results in a) healthier trees, and b) more sun getting to the plants underneath. Just sumpin’ to consider.
Here are some guidesto other shade-tolerantplants for your area.