Take a trip to Europe where oiled stocks are very common and you'll see they use oil on oil stocks.
I use to wax stocks and found they got a bit tackey and left fingerprints more than a quick wipe with mineral spirits and another light coat of oil. Wax works better on varnish type finishes.
Also note the op asked about Beretta oil finish. Beretta sells stock oil for maintaining their stocks. Not wax.
Horseman
Wood is NOTHING like metal when it comes to cleaning it off. The stuff they use to get it off auto body work prior to spraying would damage a stock. Mineral spirits is not adequate to get it out of an irregular surface, period.
Oils work differently to level out than newer paints specifically designed to repaint auto bodies. For one auto paints do a much better job of leveling without fisheyes.
Suggesting not to use wax is ridiculous. Most oil finishes, and all oils designed for maintenance, include a fair bit of oil and waxes. Oils can be applied over wax without more than a quick wipe down with mineral spirits.
Good waxes will be harder than the old standards and will not fingerprint. Even Johnson's will not fingerprint under most conditions. Bri-Wax certainly will not fingerprint.
Berretta maintenance stock oil is more wax than anything...
