If the nail is just hanging on by a thread, I'd pull it off. This way you can use your quick-stop right then to stem any bleeding. If you let it alone and the chicken pulls it off or another chicken pics at it, then it will still bleed but you won't necessarily be available right then to treat it. Fresh blood is also very exciting to pick at for the other flock members. Don't know why, exactly, but it is. I'd opt for known course of action rather than leaving something like that to chance. Then clean the wound as superchemicalgirl described. If you have vet wrap, you might consider putting the TAB (triple anti-biotic) on a small piece of gauze and securing it to the toe with vet wrap. Chickens walk through lots of bird poop and this will help to keep that stuff out of the wound area. My ranch store sells vet wrap in several colors and one of them closely resembles the color of chicken feet to it blends in and I think you'll have less pecking interest from the rest of the flock.
Dan