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I don't think you're yet in the region of proof for blaming the strop. Arm hair is a pretty easy target. Better would be to sharpen the razor, then try to shave. Then strop and try to shave. Compare...

Different strops have different amounts of 'draw' (the feel of friction as you strop) and that's normal. Why do you think your blade is getting damaged? What's the evidence for that?