As someone who has to deal with this issue a lot, allow me to add my 5c
Personally, I will only ever shoot a cat. Any other method is too cruel for my liking. I have seen poison bates left to kill a especially murderous feral who was annihilating chickens only to have the bates kill the cat and promptly a devil who consumed its corpse.
Drowning is quicker but when you consider it will take a minute or two to drown its just not quick enough.
I trap in cages and kill with a .22lr to the brain or kill in the field with the appropriate shot. It's instant and the most ethical way to dispatch an animal.
And I guess that's the point. Any way that can guarantee an instant brain death is an ethical method.

