Knives are not pre-empted under Michigan law. This means that every city. Town, township and county can have different laws about knives. Mackinac County and the towns here are mostly farm country and recognize knives as tools with different purposes. The areas you frequent here in Michigan are not as laid back.
According to state law you just can’t carry a knife with ill intent. Ann Arbor may say no knives at all. Your best bet is going to be to contact an Attorney and ask how you can carry/transport your knife legally. Be sure not to mention anything about self defense with it. Carrying a knife for self defense is illegal state wide, using one as a “weapon of opportunity” in an emergency is ok though.
I’ve never said Michigan laws aren’t confusing or counterintuitive unfortunately.