I like the "two sock" method: Get two clean athetic socks and put one on each hand. Bring along a bucket of warm water with a drop of dishwashing liquid mixed in. Dip your left hand in the water and run it across the top slat. Run your right hand, still dry, across the same slot, in the opposite direction. Work your way down the slats, wetting and then drying, until you have gotten them all.
It's tedious, but it works--and you shouldn't have to do it very often unless you live in a particularly dusty area.