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Not if it is a Gold wash!
These products will take the Gold off immediately.
But on a regular etching, I've had no ill effect from it

You are right, if they are merely cosmetic and not affecting the blade, leave the cuts alone.
To be safe though, you could lightly sand them out, using a pumice stone or some fine grit sand paper....

That sounds like a very bold and rather successful first shave.

The burn is to be expected, learning how little pressure it takes, takes a bit of time:)

The fools pass is a technique I don't...