I carefully wipe mine with microfiber cloth with a washing up liquid solution on it, then dry it off, then wipe with IPA. In theory a microfiber cloth should get further into the grooves, certainly sound and look better after a wash anyway.
I'd rather avoid the risk of running them under the tap.
Brushing, playing, brushing the stylus ... Generally after twice it's alright. A wet clean with a microfiber cloth does help though, particularly with the static.
.