There should be a few spots in MN that sell WI licensese. I know in Chicago there are at least 3 spots I can get Michigan and Wisconsin deer licenses at. I don't know if its good or bad, but Ive never been asked for my hunter safety number in WI. A few years ago my buddy was asked and he had left his card in his bag and the guy selling it, "Don't worry, I'll just punch in one until it works". Seems like they don't care to much in Wisconsin.
There is a 3 day rule, but I think if you look around your area in MN and make some phone calls you'll be able to find a license vendor pretty easily. Good Luck!