At the shop we use a red (medium) and white (fine) jewelers rouge on a sewn and then a loose muslin wheel spinning at appr. 3600 rpm to finish all of our handles.
I wouldn't put mineral oil on your stag handle. Stag is very porous and would probably discolor. I would try a neutral colored shoe polish although you might need a toothbrush to get it out if the stag is very rough. There also preservatives made specifically for collectables. One I have heard of is called, I think, Renaisance wax.
A knife or gun dealer would probably know where to get some.