I dug into this and this is what it came up with.
Basically the only humane way to do it is to bash them over the head or body with something.
Any sort of humane trap is seen as cruel, and any sort of poison is a "last resort".
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From UFAW:
"It is therefore recommended that live caught rats and mice are humanely killed,
using a concussive blow to the head. The trapped rat will need to be transferred to a sack


before delivering the concussive blow to its head."
So basically this means putting yourself in some danger even if you are totally tooled up and experienced with it all, as a trapped rat can wee on you and bite you unless you know what you are doing.
It doesn't mention shooting it in the head or elsewhere, but I guess that would be a pretty "concussive blow".
This is getting to be a topic that is animating some people, wish I hadn't brought it up, as I did, more or less just for laughs.