I would not recommend using mineral oil on leather in any circumstance, long term it will only harm the leather. There are way better options, like a small amount of pure neatsfoot oil. The best option is probably a pre-made mix of oils and waxes, like beeswax, lanolin, and coconut oil....Remember you can refresh an older strop with sandpaper and a small amount of mineral oil.
That's funny, as I would have recommended using mineral oil on horn or bone handles and scales. Pure neatsfoot oil would definitely work just as well or better though.That said, my strop is over fifteen years in my service and is in perfectly good condition. Neatsfoot oil, I now own some and would say it may at least good or better since I bought it to use on horn scales. On horn it is a good option maybe also on leather strops. However, there still is over fifteen years of a few drops of mineral oil that does just fine. So, if you have mineral oil, it works, If you don't have neatsfoot oil, you don't have to buy it.