Meerschaum is soluble in water. A Slighlty moist, clean cloth, applied judiciously, will help remove the grime. Keep in mind the coloring is permanent and arguably part of a meerschaum's charm -- it colors as it's smoked.
Never use "rubbing alcohol" on any pipe. The 70% rubbing alcohol contains a bunch of added ingredients and is nearly 30% water. It doesn't evaporate very well. The 70% is great for sore muscles and massages, terrible for pipes. The 90%-95% alcohol (NOT denatured) is fine -- if you're not sure, as your pharmacist to get the right stuff. I use Everclear, it's 190 proof and it's potable -- $10 a fifth here, but it lasts a very long time, I prefer using potable alcohol, adds no flavors, and evaporates quickly.
Unlike briars, any cake in a meerschaum is a bad thing. If this pipe has cake, it needs to be carefully removed. Keep your meerschaum "cakeless" by carefully removing the debris once the pipe has cooled and "ream" it with a clean paper towel.
Do some reading on cleaning estate meerschaums. I'll start you with this piece by Fred Bass, who is probably to most renowned meerschaum pipe expert in the USA:
http://rebornpipes.wordpress.com/2012/08/01/cleaning-up-estate-meerschaums-fred-bass/I love my meerschaum pipes. They're more delicate than briars, so they definitely aren't "pocket pipes," but properly maintained, meers provide the cleanest, driest smoke -- if you want to taste a blend best, reach for a meerschaum.
Good luck!