Cleaning wrap
In the past, i have taken a some spray starch and lightly dusted a very soft cotton t-shirt with it...not heavily, but just slightly damp. (I bought a pack of those cheap cotton Hanes t-shirts and use them specifically for this.)
Then I twist around the wrap going with the direction it is wound (not top to bottom). My cue has a very soft, courtland type linen and cleaning it in this manner has kept it feeling like new and very clean.
I'm not sure how this would work with linen that has been coated, waxed or sealed in some fashion.
-m