I've always used 99.9% isopropyl alcohol, not to be confused with the grain alcohol suggested earlier. Do NOT drink isopropyl alcohol, you'll likely end up in the ER. Not that I haven't landed in the ER after drinking ethyl(grain) alcohol before..
I don't know about a bottle of Everclear or a mason jar of granpda's medicine but isopropyl in liberal amounts rubbed over the messy area with something like a q-tip or kim wipe is perfectly safe for your boards. If it's a particularly bad mess or dirty board you can also get anti-static brushes on Amazon, but for something like the speedball you probably don't need that. Isopropyl typically does the job very well and quickly evaporates.
This is what I use:
http://www.amazon.com/MG-Chemicals-Isopropyl-Alcohol-Cleaner/dp/B008UH4AI8/ref=sr_1_5?ie=UTF8&qid=1432191635&sr=8-5