Intriguing question. How do YOU humanely dispose of a dead, or, soon to be dead mouse
As far as your idea about a trap for non-existent SHB ( small hive beetle)
make one and wait until the beetles come TO YOU, and they surely will. Then tell us.
On another subject, what do you and your fellow beeks in the UK, think about the VITA -EUTOPE Ltd. Verroa mite treatment called APIGUARD
Maybe the question has been discussed already but I haven't seen it.