We appear to be imagining different scenarios. Imagine it is freshly amputated and is still alive, or that we amputate it and hook it up to an artificial circulatory system, or indeed my circulatory system but at a distance so nothing else is connected (curious if you think the pain chance changes in that situation).
I'm sorry, I could have been more explicit. It seemed obvious to me discussing a dead hand was silly but being the internet it's worth clarifying these things.