Liz, the mice poison that you are talking about is the one that inhibits blood coagulation so, when they say that it dehydrates the mouse, in reality, what it does is liquefy their internal organs (the internal bleeding completely dehydrates them but they don't really die of thirst, they die from the internal bleeding and is a terribly painful and long death.
I use the humane traps. They are metal boxes with a lid on top that have a little window so you can see if there is a mouse inside or not -the mouse can go in but it can't come out and you don't even have to put any bait in it as, apparently, if a mouse sees a little dark hole, it would go in on its own. And then, all you have to do is, when you see there is a mouse in it, take it outside and allow the mouse to come out.