The Tipi is a plains Indian structure, while the wigwam, generally, is for woodland Indians. There are some exceptions, but in general these are the rules of thumb. If you are re-enacting in the plains, west of Pennsylvania, and east of the Sierra Nevadas, the Tipi works. The wigwam works in the Eastern areas and West Coast Indian structures are similar. Of course, there are variations from the traditional round shape to the long houses of New York tribes. Decide what you want. You can buy a variety of canvas made Tipis from suppliers, and buy the poles needed to erect them. They come in different sizes, too. The Tipi is the Cadalac of tents, allowing a comfortable pit fire inside, air conditioning, and protection from wind storms that will blow over and down other tents and structures. But, I do not think a Tipi would be a proper structure to be raised in Eastern Kentucky, or in Pennsylvania, and east . If the early journals are correct, much of western Kentucky was also heavily wooded, although today there are wide open pastures for horse ranches, and even row crop farming in some areas. If you can get a short course from your Farm Bureau office, or the local bank mortgage department, or a university Geologist, or agronomist, on how to identify woodland soils form prairie soils, a quick look at any soil will tell you if the area was originally prairie, or woodlands. That can help you determine if your Tipi is an appropriate structure to use for a temporary home at that location.
I have read extensively about wigwams made from sheets of bark cut from large live trees, and tied to the frame in layers to shed water. This can hardly be done today, as large trees are too few and too far between. Using live bark for a temporary shelter, when you can use a man-made substance( canvas) makes little sense. Just as canoes can be made with various outer shells other than birch bark, and then pained to look like they are birch bark canoes, for re-enactments, shelter canvas can also be pained to look like bark. Then just tell the visitors what the real material is, and why you have refrained from using it today. You will have taught the uniformed a bit of living history, as well as a lesson in ecology. Its not every day you get to teach the public two good lessons in one presentation.