Imma go out on a limb here and say , if you have a mouse you have many mice !!!
I dont know of any humane ways to get rid of them to tell the truth, you could get a cat ? but that can take a long time.
My dad buys poison at canadian tire, and puts it out of reach of other animals etc, like under the washing machine etc, and when they eat it it makes them thirsty, so they go out side in search of water and die outside.
We have had mice in the past and that is the only way i know to get rid of them, i dont think that those traps you set are good, since you have to touch the mouse to get it out of the trap!! which as you said they could be carrying anything !!!
But i have to say in a cold NL winter who could blame the mouse for wanting to come inside huh ?
Goodluck tho !!!!