I'm not sure I understand your questions. Of what relevance is the convertible as opposed to another type of car? I suppose there's the danger of being rained on.
As long as you obey the speed limits and other rules of the road, and your convertible is not stolen, there's no reason for you to have an encounter with the police in either State.
However, if you have IL plates on your car, and do happen to get pulled over in WI, being polite will go a long way. Having grown up in WI, I can tell you there's an unfair stereotype of IL tourists being rude, even to police officers.