To the OP,
Just be aware that there can still be some very chilly nights that late in the spring or early summer months. No snow or ice though. The Great Lakes have not warmed up yet from winter deep cold and tend to keep the air chilly up there. Bring warm clothes incase you encounter some cold days and/or nights as you will be coming north from a very warm to hot area in late May and it might be a shock to your body. Summer really doesn't begin in the U.P. until mid to late June but it's still warm in October as the Great Lakes are now holding the summer's heating that rises and blows across the land. Then again, you may have some temps in the 80's during the day for a high! Varies a lot from day to day or week to week due to weather fronts up there in late spring.
You will be well ahead of the crowds that go to the U.P. and that's in your favor, however, many of the trees may just beginning to get their leaves so it looks very different than just a month later in the year when the forests are very lush. The U.P. is simply gorgeous anyway 12 months of the year!