I would say that if you do a deep mulch method and keep it roofed so that no water gets into the mulch, then clean it out periodically and compost it further away and put the compost where the plants can get at the nitrogen, like in your garden, then you should be all good. Chicken poop is worth thinking about, it can be more pathogenic than other horse or cow. the nitrates can be an issue with any animal if there were a way for them to get into the ground water, but that usually takes a lot of waste. human waste in comparison is the most pathogenic to us, so another order of magnitude altogether.
I've studied waste management informally, especially natural systems like the reed bed system in Acada CA. when the waste is spread out and mixed with composting material, the nitrogen cycle is sped up and transformed into the least toxic form and made available for plants. if you have a good bit of vegetation it will typically speed up it's growth to match absorption with rate of production.