Mist is not a good idea unless you want lung problems breathing in the cloud of liquid.
Look at the Fogbuster type systems which is what I have made that have the air independant of the liquid so you are dribbling a bit of lubricant and clearing/cooling with the air, though it is mostly a lubricant/swarf blower.
I think it is in my “further advantures thread” look or search for peristatic pump, should not be too many occasions when that comes up.