Baby oil is available everywhere online and in most places you go to buy groceries. Just look for the personal care or diaper aisle, and you’re sure to find it somewhere in the area.
Mineral oil is very similar to baby oil. It’s probably a better alternative to clipper oil because it doesn’t come with polarizing scents, and your specialized clipper oil is essentially a more refined version of mineral oil.
If you must, you can also use silicone oil as a clipper oil alternative. One negative aspect of silicone oil is that it tends to trap dirt more easily than baby oil or mineral oil.