So I guess by 'drying' they mean oxidation ruining an oil's fluidity. Simply adding antioxidants will only delay oxidation.
On the other hand using saturated fatty acids will avoid oxidation. Unfortunately longer saturated fatty acids will solidify at warm temperatures.
Coconut oil makes some sense since it mostly has saturated fatty acids of medium length, though apparently they are still a bit too long for cold weather.
Shorter fatty acids will have increasingly lower melting points and increasingly larger vapor pressures(and so might actually dry, ie evaporate, if present as free fatty acids).
Evaporation should be much less of a problem with triglycerides.
So an oil consisting of triglycerides of medium-short saturated fatty acids is a good avenue to pursue if you are looking for something patently nontoxic.
Trihexanoin has melting point of -60°C and the next natural size up, trioctanoin, has a melting point of around 10°C whereas tridecanoin has a very warm melting point of around 33°C.
These melting point are for the pure chemicals. If you have mixed triglycerides then the melting point can be much lower. The point is just that fatty acids with 6-10 carbons seems ideal.
They sell such stuff in health food stores under the name MCT oil. So it isn't outrageously expensive. Basically it is coconut oil which has been fractionated to remove the larger and more lucrative lauric acid and contains triglycerides of mostly octanoic and decanoic acids. The melting point is around -4°C. This could be lowered quite a lot more if transesterified with a source of hexanoic acid.
The most salient concern I have with this strategy is that moisture will eventually break the fatty acids off of the glycerol and will then evaporate and be a little stinky. I don't know whether this would occur fast enough to matter. This hydrolytic rancidification is the primary way that butter develops off odors, but butter is an emulsion and so has tremendous exposure to water.
Microbial degradation is another potential concern. These are natural triglycerides so microbes have the machinery to break them down. However oils in isolation tend to be fairly resistant to microbes since there is no ready source of water and other nutrients besides.
These triglycerides are small enough that they will boil around the same temperatures that other oils would smoke. 230°C or so. This is probably better than smoking but you would be concerned with loss of oil over time. Compare soybean oil which has a smoke point of around 260°C and a boiling point of maybe 300°C.