Looking at the photos in the link you provided, I can see hammer
marks - they aren’t completely smooth. If you want the piece to be
smooth, you can sand it. 3M makes wonderful sandpapers, mentioned
With practice, you can learn to hammer leaving few marks. When you
hammer metal, however, the metal will move - the wire will flatten,
get wider, etc - which is the point of hammering anyway. So I’m not
sure what you mean by preventing the earrings from changing shape,
but certainly a circle of wire can be hammered, and remain a circle.