On leather I just add a bit more of the abrasive spray when necessary. Leather on alcohol is pretty harmless, drying more rapidly than water, but it can eventually loosen the glue attaching the strop to the paddle.
On nanocloth you can refresh with a water mist, although I rarely do this. If you are being picky I’d suggest deionized water, which is less likely to produce particle agglomeration which could be misinterpreted as a more aggressive finish from the clumped or agglomerated particles (larger micron size).
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Ken