Can I run a ground wire along the outside of conduit?
Absolutely, you can run a separate ground - they have allowed this for a long time and have recently liberalized the rules on retrofitting grounds to practically everything else.   So if you have other outlets that could also use a ground, food for thought.  

The grounds do not need to follow the same route as the original wiring.  They do need to be thick enough for their purpose.  Also, other circuits can share a ground wire, as long as they originate from the same panel.  

Should you do it? Absolutely!  The problem is, right now you have the NEMA 10 problem.  Normally if a neutral wire breaks, the neutral wire is pulled up toward 120V because power has nowhere to return, but we don't care because the grounding system still protects us.  Now,  if ground is also the same wire (like in NEMA 10), it too will be pulled up toward 120V - and now things which are supposed to be grounded will instead shock you!  Including switch plate screws, metal chassis of equipment, and of course, the metal chassis of your subpanel, which you will be opening directly when you realize there's a problem.  Touch that and a water pipe, and blammo!