This is a reasonable request from OP. A few months ago I bought a roughly 100 year old knife with wooden scales. The scales were dry as dust and seemingly unusable, and underneath the scales the tang (and the bolster) showed major rust pitting. Meaning the knife handle had been seriously wet for a long time before being dried out.
After popping the scales off I decided to soak them in water for a day to see what they were. The water turned really dark and the scales re-hydrated, to the point that there was usable wood again. At that point I decided to use a little bit of the original scale wood in my rehandle job thinking that that original scale wood was maybe at least 25 years old when used as a handle on my knife in 1920 and possibly even older than that. So the scales are something I want to keep.
So, for OP's question; some of the "oil" or grease, or years of crap built up on the handle can be removed with warm water and dish soap. And any excess moisture should be removed to protect the steel. But that oil or grease or crap will also protect that wood handle and add a certain patina to the wood which, IMHO, is a positive thing.