A bit late to the discussion, but I have a question: Why do you need to "clean" the grinder at all using soap or any chemicals? The best solution offered here seems to be to a) take it apart and brush off the coffee dust, and b) use vegetable oil for the rest. I assume that the oiled grinder will have a few rounds of throw-away beans run through it before use to suck up the oil (defeating the purpose of the oil?)
Here's what I do for your consideration:
1-Take it apart and wipe with a clean, dry cloth as much as possible.
2-Reassemble and run a couple batches of dry oats through it to collect stale oil.
3-Run one small batch of throw-away beans through to flush out the oats.
I don't remember where I read about this cleaning technique, but it works for freshening up the machine, eg, removing stale oils. Beyond that, it is a used grinder--who is expecting a factory new gift?