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You can get a natural sponge from a craft store, or Wally Mart in the craft section or a body bath type store.

Or try a synthetic tile sponge from Home Depot and cut to the size, they are super...

Yes you can but the hard part is holding it flat with all the hardware and secondary strop if it has one.
I use a length of Para cord looped around an open doorknob this will put your strop at waist...