For those that live where firearms are illegal to discharge or that do not own a gun, might I suggest a pellet gun. Not one of those that are toys but a .17 or .22 caliber with enough power to quickly dispatch most varmints such as rats, squirrels and coons quickly. If shooting is the answer, a good pellet gun will not only serve but is legal within most, if not all, cities, counties and states.
Now as to cruelty. Let me say that drowning is fairly quick and easily within the capabilities of an ordinary person.
For those that advocate taking the trapped animal to be disposed by others or waiting for it to be picked up and disposed of, what you may not realized is how traumatic it is for a wild animal to be caged and/or transported for hours and possibly longer before being disposed of in a "what you hope" is a humane way. There is physical trauma and there is mental trauma. I, for one, do not consider a quick death by drowning as soon as possible after capture as cruel as hours of being caged and then killed in another fashion especially when you consider that a bullet can miss by a fraction of an inch on a small animal and it can suffer longer than drowning takes.
Even releasing the animal in another area could in some cases be considered cruel. You may be relocating that animal in a territory already overpopulated by the same species or one with a similar diet. Some species are very territorial and may even maim or kill the intruder.
There is no easy answer to the cruelty question. For many humans it is an highly charged emotional topic and that is apparent in this thread. I do not know the circumstances of the man, wife and squirrel so will not speak to that.
I do value any reasoned response to my post but please, no shouting and name calling. I am sensitive and have a tender heart.