If the car came from factory with the tires offset, you are going to want to change out the worn out tires with a like size and not rotate the tires out. While what you said about moving the tires are is a normal process, you won't do it with tires that are offset. If you were to change this out with having the wider tires on the front and the skinnier tires on the back, I don't think you'd have stability issues, but it is going to feel wierd (different wierd). Other considerations of doing this is that you'd more than likely have different rim offsets to accomodate the different size tires. The rear wheels probably will not fit on the front end of the car, as well as not being able to fit the tires in the first place (rear wheels may be too wide to support the front tires and rear tires may be too wide to fit on the front wheels and have the support they need).
Bottom line is, replace the tires you need keeping them on the axle they now reside. Any decent tire shop is going to know this and not try to swap them out as is the norm. If they do suggest you do this, I'd highly suggest you find another tire shop. Giving you another situation of the same, consider a Corvette which has offset tires (18" front/19" rear). As an owner, you'd not allow them to swap out these tires. Your car is no different.