I just gently pick off any clumps of dried poop off their behinds; I always do end up pulling some fluff out, but they don't fuss much about it, and - pulling a bit of fluff off actually helps the poops not stick nearly as much. I've done this for many, many years with no ill effects whatsoever.
No one has mentioned thus far, but the best course is prevention, if at all possible. Many feel the reason chicks get pasty butt is often twofold; using low quality feed, and/or the brooder being too warm. I can speak to the low-quality feed and confirm that every time I switch back to a brand that is known to not be "top shelf," I DO see more instances of pasty butt. I cannot speak to the brooder being too warm, as I don't (wouldn't) take chances on experimenting in that way.