My mechanic told me they had rat problems all over the garage in winter, they came in from the cold. Someone told him to put out bowls of real, sugared Coke for them. Pour it slowly to save most of the bubbles. Said that the rats drank it and could not belch, the pressure on their hearts killed them. He said he found dead rats around for a long time.
I have no idea if it would work for mice, but worth a try. Dogs and kids could drink it with no more side effects than normal.