I would be careful not to let any liquids get down inside the grinder body and damage the internal components. Aside from that I would maybe try a dilute solution (dip a scouring pad/brush in the solution then scrub). I wouldn't pour anything into the grinder obviously.
Another approach may be a solution of descaling solution. Either way you'll need to be sure to get everything rinsed (wiped several times with a water only sponge/brush rag) to remove any residue.
My Super Jolly came in a similar fashion; luckily they seem to clean quite easily (at lease mine did). I'd try a stiff nylon brush first (dry) then go from there. I'll bet most of the gunk can be scoured off without the risk of adding liquids to the equation.
I'd soak; scrub then immediately dry the removable parts. I do on a very infrequent basis (to avoid rust problems) and have gotten by just fine making sure I dry everything right away.
It can be a fun and "interesting" project; good thing is that in the end you'll have an amazing grinder that's well worth the elbow grease now!
