Transporting a critter is not "dumping them on someone else"...especially if no one else around has chickens. Besides, no one said to take them and release the thing in front of someone elses home/property. Everything has a purpose. People seem to think that theirs is to rid themselves of anything they don't like because it bothers them...permanently. What're we going to do when the world gets so crowded that there's no such thing as being allowed to have more than a half an acre for home and property? Start offing the neighbors who 'crowd' us?
Drowning a critter is just wrong. It's slow and extremely painful. A very' hammer to the head is better than drowning.
As for once the thing is dead, if you have vultures, throw the carcass in the middle of an empty field for them (or just anywhere in an open area where they can spot it easily from aloft). It'll get cleaned up in no time and no worry about smell. If you don't have many vultures, then the freezing idea sounds like a darn good one!