I use raw linseed oil (AKA flax oil) from the grocery store. I use it in food and keep it in the fridge. If a bottle goes past the expiration date, it comes out of the fridge and gets used as a wood finish.
I don't want those chemical additives on my tool handles, which is why I avoid using BLO. With raw linseed oil, there are no nasty chemicals to get onto your skin, so I skip the rag and apply it directly to the handle with my hands. A square or two of toilet paper wipes the excess oil from my hands (and get flushed), before washing hands in the sink. No rags, no diposal problems, no fires.
For bigger jobs, I keep the raw linseed oil in a large jar (from applesauce), big enough to hold a dedicated paintbrush (1.5") that's also stored in the jar with the oil. The paintbrush handle was shortened to make it just fit in the jar, so the lid will still screw on. The brush applies the oil, and it's rubbed in by hand.