Dave, I investigated the Fiebing's Pro Dye and the oil part. What I found is that the Pro Dye does not have oil in it, but rather that it is more compatible with oiling leather than their regular dye. If you notice, the current packaging does not say, "oil" on it anymore.
Yes, I do use the Pro Dye with my leather work most of the time. Good stuff. It is just not light-resistant on anything but leather in my experience.
James Rogers has vastly more experience than I do with that Pro Dye, so you may want to check with him.
God Bless, Marc