There's a temptation to over-complicate things when it comes to lubrication. At the fundamental level, viscosity aside, mineral oil is all much of a muchness, and derives from a base stock which varies slightly depending on where in the world it was pumped out of the ground.
A hundred years ago the origin of the oil was considered important, because certain varieties, such as those from Pennsylvania, were considered to be of superior quality. These days the game changer is the additives that are mixed with the base stock to improve and modify it's characteristics, such as VI improvers (irrelevant in a SA hub gear!), anti-foam agents (also irrelevant) and detergents.
Most of the chemistry is added in order to improve the oil's performance at high temperatures, increase service interval mileages, and hold minute particles of combustion solids in suspension rather than let them build up into lumps.
For a low temperature, lightly loaded application like a Sturmey hub gear, the operating conditions simply aren't severe enough for any of this stuff to matter. It just needs to be oily enough to maintain a film between the metal parts, and not so thick & gooey that it jams the pawls and prevents them from working cleanly.