[Joe Demko]

Since your chemistry isn't all it could be, let me point you in the right direction.
The basic rule for solvents/solutes is that "like dissolves like." Polar solutes require a polar solvent. Non-polar solutes require a non-polar solvent. Water, due to its partially polar nature, is sometimes described as a universal solvent. Ballistol doesn't dissolve in water, though, it forms an emulsion thanks to some of the ingredients.
So, what you need to do on this pointless little quest of yours, is find an appropriate solvent for mineral oil. Mineral oil is a non-polar hydrocarbon. Benzene and carbon tetra-chloride are a couple examples of non-polar solvents.
You'd be much better served just to switch to a different product than to try to "thin" Ballistol with something other than water, Dr. Science.