I bought a 3M adhesive metal hook and hung it on the wall in our bathroom. I hang all three of my strops there by the sink.
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I use a 3 M adhesive hook--plastic, not metal--that I put on the end of a painted wood shelf in my walk in closet near my bathroom. Pefect heighth, etc. I also have three strops hanging from that one hook.
I would never keep my strop in my bathroom Way too humid for it!