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Alex, to answer your original question. Yes strop on you linen or equivalent to clean the blade of soap, oxidation, skin and blood before stropping on leather.
If not then all that crud will imbed...

Don’t know what artificial leather is or what it looks like.

But I have pasted Craft Foam, Nylon, woven Polyester strapping (seat Belt type) and Polyester Sailcloth Canvas and cotton canvas with...