Hi,
A likely cause of diarrhea in a stray cat is intestinal parasites. There are several different ones so I would try to give him a broad spectrum de-worming product. Panacur is a good one (it kills roundworms, hookworms, and tapeworms), but it may only be available through a veterinarian. You could ask and see if they would send it with you without seeing the cat if you explain that its a stray. Otherwise, Strongid is a good product for roundworms, which are probably the most likely culprit. Mix whatever product you try with a small amount of canned cat food. This usually works well.
Personally, I would not recommend trying to trim his nails. Anytime a pet is only partially sedated or tranquilized there is still a good chance of getting bit. If he isn't tame enough to do it without medication I just wouldn't do it.
If you have further questions let me know. If this answers your question please click accept. Thank you and good luck!
Lynn
Veterinary Assistant
worked at a vet clinic for 15 yrs, BA in biology, have had cats most of my life