i would euthanize the poor thing. clove oil or like someone stated, put him in a bag or pillowcase and slam him on the floor--sounds cruel but its instant death.
I haven't found any reason to close this thread yet, as long as you guys keep it civil, no need.
There are many ways to kill your fish quickly. Which one makes you feel the most comfortable is whats important though. You almost have to detach yourself to do the task. Cutting off the head or smashing it would probably be your best bet in this situation, since its an eel and all. I'm sorry for all the heartache you will have to endure, wouldn't wish it on anyone. Best of luck.
definatly dont freeze it that isnt instant try to chop the head off clean and quick if you do it right, and dont whack it on the floor that is horribly mean. personally i wouldnt be able to whack my fish on the floor to kill it.