From my experience, the clay bar will not remove any scratches or swirls in the paint. I have used them numerous times on cars, and they remove contaminants in the paint that wax does not remove, such as small particles that fall out from the atmosphere. When you use it, the clay turns dark as it picks up the dirt. Afterwards, the paint feels smoother than you can imagine.
For scratches and swirls, I really like the Harley swirl and scratch remover. It seems very gentle for light marks. If that isn't strong enough, use a little 3M rubbing compound. I always use these products by hand, expecially on a bike since the surface area is small.