Most quality 'honing oil' is mineral oil (Smith's 'honing solution' is an exception; I think it's a detergent-based solution). In fact, Norton sells a very good honing oil that's nothing but 100% mineral oil at a nice, light consistency/viscosity, and certified as food/kitchen-safe to boot. Home Depot carries it, alongside the Norton 'Economy' SiC stone they also carry.
The 'laxative grade' mineral oil sold in pharmaceutical sections at grocery/drug stores is a somewhat heavier (more viscous) oil; but it's often used in place of so-called 'honing oils', and it's pretty inexpensive as well. Could also use so-called 'baby oil', which is just mineral oil with a scent added.
'Sewing machine oil' and the stuff used for electric shavers/hair clippers is also just light mineral oil, and could be used just the same as the others mentioned. I've also seen it labelled & included as a lubricant for electric paper shredders (I have a bottle of it that came with my shredder). It's all just mineral oil, and any of them will work for use on sharpening stones.
David