hmm... Since I have an absolute phobia to dead and dying stuff... I don't touch dying fish.... I would let them die at their own pace in a quarantine tank. then I'll dig a hole deep enough in the garden and pour the water+fish into the hole and bury it.
And is this your view of humane? What if the fish is slowly suffering as it dies? In this case, wouldn't it be more humane and compassionate to smash it with a hammer?