I'm a wee bit more up market than veg oil, it's tesco's "ground nut oil" for me, as thats what I use. Veg oil is fine, especially if your planning using your O1 carbon blade for food prep and or eating. For applying the veg oil an oily rag is the way to go, and again veg oil is safe, so no issues stowing the veg oil rag in a trouser pocket, there's heath issues associated with prolonged exposure to mineral and some synthetic oils, "particularly bad for a man"; as my old granny would say
WD40 and similar is good for cleaning up steel, but it evaporates surprisingly quickly, if you do use WD and plan to stow the item, wipe off the WD after cleaning and wipe down with lub oil, 3:1 (or veg oil) etc as that'll protect it far longer.