Is that a cassette? I'd think a freewheel instead. But there are all sorts of oddball stuff from back in the day that I've never seen.
Whether freewheel or free hub and cassette, the bearings, pawls and other internals only see action when coasting. So you really only need a corrosion preventing coating on the internals. Most any light oil will be good enough IMO. But if you think you need something that sticks to your ribs more, then any very very light grease you care to use.
Too heavy or too much grease and the pawls may not engage quickly or not at all.