Egyptian shimmies are stable shimmies. These are shimmies you do while standing, flat footed and layered. (see other videos or how to layer an Egyptian shimmy).
the key to doing a perfect Egyptian shimmy (knee shimmy) is to use only your knees, which will work your quads without moving your hips keeping the feet flat as much as you can. If you engage your hips while you do an Egyptian shimmy, you will not be able to layer easily, so remember that.
Watch the video on the basic technique of an Egyptian shimmy: