"3-in-One" debuted during the first great bike boom in 1894, making it one of the oldest cycling products you can still buy. The oil was originally intended for bicycle chains, and the name indicated it "1) cleaned, 2) lubrcated and 3) rust proofed", hence, 3-in-One. After 115 years, it's still not a bad choice for chain lubration.
3-in-One contains a vegetable based component, citronella oil (ever notice the way 3-in-One smells?), which will go rancid, break down and turn into very much a non-lubricant. This residue would get cleaned off a chain in the next application, but when enclosed in a small metal shell it has no where to go. Probably more American Sturmeys have been rendered inoperable by 3-in-One residue than for any other reason. The 3-in-One folks themselves do not list hub gears as a potential use for their product.
Fun fact: In the 1920s, pioneer American Birth control advocate Margaret Sanger was married to then president of the 3-in-One Oil company, J. Noah Slee. She smuggled illegal European-made diaphragms into the USA in secretly coded barrels of the citronella oil imported by 3-in-One.
The blue can of 3-in-1 I linked to is 3-in-1's motor oil or turbine oil, which is supposed to be different from regular 3-in-1. I don't think it has citronella in it. I was taught to never use regular 3-in-1 in motor bearings, gears, pump impellers, or rollers because it would gum up, which would seem to be from the citronella.
How about oil? I've seen the following recomended, all of which seem reasonable:
20wt motor oil
30wt motor oil
10W-30wt synthetic motor oil
automatic transmission fluid
75W-90 gear oil (note: the viscosity of gear oils is measured differently - this is NOT "three times as thick" as 30wt motor oil)
75W-90 synthetic gear oil
sewing machine oil
Of these I'm personally attracted to the 75W-90 synthetic gear oil. It's locally available in quarts, it's not terribly expensive, it has extremely long shelf and service lives, it's designed for use in non-pressurized lubrication systems and as a purpose designed gear lubricant it has anti-sheer additives.
I have gear oil, too. Just not sure how to get it into the hub. The zoom oil is very similar to sewing machine oil.