A couple things. There is no reason to drive into the city limits of chicago if you passing through. The 294/290 bypass keeps you outside the city at all times from Wisconsin to Indiana.
You are not going to have a firearm in the car, so it would be a major stretch for them to tear the car apart looking for something when you answer the question about having a weapon in the car in the negative.
People killed by:
MN permit holders 3
MPLS Light Rail 9