If I'm going to oil a 50 year old appliance without taking it apart to clean it, I use Marvel Mystery Oil. It melts the old dry oil, and will not dry up again.
3in1 Household oil is not for motors, but they do make a 3in1 20W non-detergent oil that would be ok. For a lighter oil, Sewing machine oil or Zoom Spout (turbine oil) are excellent.
WD-40 is NOT a lubricant, it's designed to displace water, that's what the 'WD' stands for.
Nice mixer, I have a Hamilton Beach Mixette, but the Sunbeam Jr. looks even nicer.
Ken