are mortal enemies! That's the quickest way, oil wise to ruin a good scabbard. Mineral oil has such a high viscosity that leather just soaks it up like a sponge. When you see limp, dark leather scabbards and sheaths, someone has put something kin to that or some sort of machine oil on it. As for putting it on stag, I can't see that either unless your looking for sort of a translucent sort of look as it (stag) will soak it up as well over a period of uses. I'd use Renaissance wax on the stag.
Both stag and leather are most easily damaged by two things: heat and UV. Leave'em in the sun for very long and you can count on faded chalky stag and brittle leather.
As for your leather, I use "Cavalryman's dressing". My ex-father-inlaw, now deceased, (my x-wife's oldest brother and my own dad are but 9 years apart! she was the youngest of nine children) told me how to make it as he served in the U.S. Army Cav. up in Chicago of all places in 1938. They still had and maintained horses. He told me part of their duty was to mix up a dressing that was three parts bee's wax and one part neatsfoot oil, (NOT neatsfoot oil 'compound'). The finished product when cooled is the consistancy of soft shoe polish. you heat it up till clear, paint it on and warm it over a stove to have it soak in. Truthfullly, it's more or less the same thing as "snowproof" dressing but very cheap to make up. It leave your leather waterproof and imparts a nice golden color to tooling/harness leather not to mention it smells great.
regards, mitch