I don't think "fossil" ivory would retain any oils. Very fresh beach-collected walrus ivory might. Ivory, very dense, hard, and when well-polished "feels" oily, but that is imparted by the natural oil in your skin. I have to agree with Bill D.

My wife bought an ebony box with a part missing. I obtained some ebony that matched in color (some has brown streaks) and started to do the first cut before I shaped it. I didn't get sawdust; I got carbon and a hell of a burning odor- I was burning my way because of the friction from the saw. The odor stayed in the workroom for days. It took me a while to figure out how to handle the material before I got it right.