There is no reason to be scared to attempt this, you really can't cause much harm as long as you don't use something with a coarse grit. I never use anything coarser than fine Scotch-Brite (if there are deep scratches), and then I polish some sort of polishing compound, a Cape Cod cloth, toothpaste, Polywatch, or whatever else I have lying around. It's just an acrylic crystal, don't get too precious about it. As long as you remove the scratches and end up with a nice clear crystal, the job is satisfactory.
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