Nice and to the point, but that may do bad things to it. I tried cleaning my wrap out that way (16 yr old linen wrap, smokey and a bit dirty) and it ended up looking frayed. Mike Webb cleaned up my cue and re-pressed the wrap, ended up good as new. Clean no smell and felt like a new one.
I'd bring it to a cue repair person, they'd be able to get it cleaned up for cheap money.