Unlike with a clap trap for a rat (or mouse) which in one blow broke the neck, you have in a cage trap, cage or run trough trap a live specimen. How do you execute it? That is not always easy.

I remember from my childhood a cage trap with two inputs (like fyke), wherein often a lot of rats simultaneously ended up. Which was then put into a large bowl with soapy water used in the wood-fired washer, under some bricks. In my memories, the animals remained incomprehensible long underwater walking back and forth and gnawing at the bars. It seemed to last for minutes rather than seconds for drowning. But perhaps my youthful mind was very impressed and not as accurate in the timing? Rats can hold their breath for three minutes and keep swimming until three days.

A large run trough trap fits not in a bowl. If you do not have a stream or pond nearby it is a waste to have a bath to run full for drowning rats.

You can shoot them, but they are not waiting and hard to hit through the meshes. You have to wait until the rat just unfortunately happens to come under the barrel or arrow.

Impaling is possible. But in that case, the same applies. Use 2 large skewers. The first striking jab is often a fluke, and not fatal. But then the rat is pinned. With the second rod or spear you can crack the skull.

Maybe you have a dog who knows what to do?

I once threw poison in the cage. But the rat didn’t touch it for days. It has lasted more than a week before she died. And I do not like poison.
A few times it has happened that the rat after 24 or 36 hours (I do not know exactly when she fell into the trap) was naturally dead. Due to the stress of captivity, I suppose. But that is certainly not the rule.

More practical is a fireplace poker or squeegee, a rod that is bent into L - shape. That you can hook through the mesh. It gives you a greater range, because you can turn it 180 degrees in the basket. You can bet that a cornered rat attacks. If you insert a 2nd bar in the same neighborhood in the basket the rat will (also) attack immediately: grabbing it and remain biting there. Once they come under the poker you ram it down. You don’t hit always the first time the neck or skull, but usually the backbone. Then you can immediately strike the brain with the 2nd rod. It seems to me one of the most efficient methods.
It all sounds terrible, and it is. In addition, they can be pretty screaming. Even if you're just coming closer.
But the animal rights activists who are thus stepped on their toes are always welcome in the event of disruption of the caught rats to pick them alive.

The rat in the picture died after (I guess) less than 24 hours in the cage.
Many wild (free) animals die in captivity. Within three months after the capture 53% of the surviving dolphins die. Some platypus die already the day after they are captured. A wild "house mouse" in captivity usually does not survive long.

Alone you go faster, along you get further.