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I agree- wood handle brush or if you're set on wood strop, you can do a paddle or loom strop.
For brushes check out the classified here (or contact pixelfixed, wallyeman, harrywally). For paddle...

I found it very awkward to use my Neil Miller and Kanayama at first as they do not have handles or d-rings.
However like anything else, I'm getting more used to it the more I use them.
I still...