I agree. Never release a trapped predator. It is usually illegal and at the best, you are releasing a trap-smart predator to cause other people problems.
I personally have no problem drowning a predator. A shotgun will blow a hole in your trap and likely ruin it. A rifle slug can easily riccochet and, unless you really know what you are doing, it is pretty easy to wound the animal instead of cleanly killing it. There is a lot more fur than body under there. At least drowing is pretty quick, very sure, and of minimum danger to you and others.
Depending on where you live, you may be able to call animal control and talk to them. In some areas they may take it off your hands. One of my neighbors is a taxidemist. He will take trapped animals from people. I don't know how legal that is, but you might look in the phone book under taxidermists for your area.
As far as other raccoons coming in, yes that is a probability. If you have one, you have more in your area. Raccoons are territiorial. It is not so much that they keep other raccoons out of their territory, but that they make regular rounds in a specific area. You may have caught one on the move looking for a territory, but it is very likely that the specific raccoon had your area in its regular territory. If you remove it, then your chicken coop is possibly not in the territory of any raccoon right now. Another one will eventually claim that area as its territory, but that might be tomorrow, next month, or next year. By removing this one, you will have made it safer for your chickens. I'd still leave the trap set for a few more days to see if there are more visiting you.
Good luck!