As far as human safety of mineral oil goes, you will find it stocked at drugstores in a grade suitable for human consumption. (It's a laxative.)
Mineral Oil has a flash point of 170C (335F), and a boiling point of 310C (590F) A typical transformer oil (Conoco/Phillips 76 Transformer Oi) has a flash point not much different > 293°F / > 145°C. As I understand it, neither are classified flammable under the relevant US classification scheme because the flash point exceeds 100C/212F.
According to Conoco 76 Transformer Oil MSDS, you can drink it as well: "Ingestion (Swallowing): No harmful effects expected from ingestion."
Although mineral oil may not be as good as transformer oil for heat conductivity, it's still quite usable as a coolant. Heathkit made, starting in the 1960's, a high power 50 ohm transmitter load, the "Cantenna" consisting of a carborundum resistor mounted on the lid of a 1 gallon paint can. The purchaser assembled the kit and locally procured a gallon of either mineral oil or transformer oil to fill the can.
http://www.repeater-builder.com/test-equipment/heath/hn-31-cantenna.pdfHeath's time versus dissipation plot below shows the difference between mineral oil and transformer oil. Over a long enough time, no difference, but a considerable short term difference.
Higher quality dummy loads, such as those manufactured by Bird Electronics, use silicon-based oil as I understand it. Not sure whether that was the case in the 1950's though.
I have a Cantenna that's 45 years old, still has its original fill of mineral oil. Not the worlds best dummy load, but certainly adequate for many tasks.