No problem, however mention that to the agency when you pick up the car. There are no restrictions to driving to CH (there are restrictions only for Eastern Europe). The only thing to be aware of is the exorbitant Swiss prices. I'm sure you will appreciate driving back to the Italian side for dinner after being gouged for lunch and everything else during you day trip to Switzerland.
Since CH is part of Schengen, there are no border controls anymore. The vignette is necessary only if you intend to drive on the freeways.
The "cardboard clock" mentioned by the previous poster is called DISCO ORARIO. In areas where required (where parking is limited to one hour or two, for example) you just use it to indicate the time of arrival at that parking spot. It's widely used throughout Europe, including Italy, as a method to enforce timed parking. In America the time parking enforcement is done by marking your tires with a chalk, in Europe they use the "disco orario". You don't need to buy it, as you rental car almost certainly will have one already on the dashboard or windshield. I've never rented a car that didn't have one already.