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Those scratches shouldn't do any harm, but I'm also not a fan of the visual of them, higher grit wet/dry sandpaper will get rid of 'em; I always use some to get rid of my DMT scratches

The DMT will do just fine, I think plenty of folks use it that way, so I wouldn't worry about not using a Thuringian slurry stone.

Out of curiosity, do you prefer to finish on plain water or light...