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A lot depends on the condition of the blade, the number of blades and how long you leave in the tumbler.

If the blade is not that rusty and you only put in one blade and not leave it for too long,...

Yea, pumice works, as does Diamonds you just want uniform or wet and dry.
Look up Wolfpack34’s recent razor post, it is some of the nicest satin finishing I have seen, he is using Crocus.
Read the...

Yes, you did get lucky, I would have thought the rust much deeper.

If you want to remove all the pitting you will lose some etch, I would leave some pitting and keep the etch.

When you sand go...

So you don’t care about the etch?

Cut off the rust with a single edge Razor blade to see how deep it goes, clean with WD40 and steel wool.
Then hand sand. Start with 320 and go up or down from...