I sharpen my tools to great effect with 3 in 1 oil. It's just general purpose lubricant oil, nothing special.
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I second this. When I have my bevel totally flat against the stone, eventually it will begin to float over the surface, making no noise or tactile feedback. At this point, I use a lint free cloth and a bit of mineral spirits to clean it.
Mineral spirits will clean it in a jiffy and doesn't need to be fully rinsed before adding more oil, because it is oil (volatile oil).
I don't know what smiths is, but I've seen a lot of people using arkansas stones fairly dry. They need to have enough oil on them to actually float out particles. I use light mineral oil.
There's a million ways to use them. I've talked to someone who refuses to use anything but spit, because he thinks he's re-enacting something historical and saving money.
If it feels like the razor gets suspended above the stone in heavy oil, you can just use additional pressure.