I think a Cherokee style bow is a good fit for that stave. But you should know that Cherokee bows do have a gradual width taper. The taper may be less than with other types of bows but it is there. If you were to make a bow with no width taper at all, then the excess mass at the limb tips would render it extremely sluggish.
It kind of sounds like your getting too caught up in your research. That's understandable seeing as this is your first bow, but one thing to keep in mind is it's just a piece of wood. You can't learn everything about making bows without actually making some bows, and your gonna make some mistakes. I guess what I'm trying to say is just go for it already. If your first bow doesn't turn out just how you want or it breaks, you accept it and learn from it. Try to figure out what your mistake was and once you do move on to the next one. Your failures, when properly examined, will teach you far more than anyone on here can.
Don't get me wrong, I'm not saying that you shouldn't do any more research. I'm just say that at some point you just have to dive in. In the meantime, I recommend you get a copy The Bowyer's Bible Vol. 1 if you can.