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The bottom picture looks like either a rusty fingerprint or a pattern from whatever you used to wipe the razor with.

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Fingerprints are acidic and can rust steel, even under oil. Unless you...

I would also try a good alcohol wipe first. Then Ballistol lightly rubbed around with a scotch-brite pad. The latter might dull the edge a bit. I wouldn't use the Dremel except as a last resort. Not...