Skip the oil, apply pure carnauba wax (quite hard) with a buffer, or else buy softened carnauba (the stuff I prefer for softened is softened with turpentine and hasn't been made in decades, evidently.) Modern mixes may use solvents other than turpentine, as that has become unpopular or highly regulated as a VOC. Clear paste wax is the generic product, but you'll have to check if they admit what wax they are using. Beware of buying "amber" paste wax, you don't want that.
The hard carnauba applied with a buffing wheel is commercialized as the Beall buffing system, (just a happy customer) but you can "build your own" with sewn cotton buffing wheels and hard wax. Friction heats it up and melts a thin layer on.
As stated in comments already, mineral oil won't dry, though the pharmaceutical grade commonly available at the drugstore should not yellow, and "baby oil" is pretty much the same thing with added scent (or stench, depending on your nose...)
All the various hardening oils I can think of (linseed, walnut, tung) do color the wood.