Wall light switch in pantry, moving to cabinet side
You have two questions.  To the first question of how to get the wire out of the existing box, you would mount a surface-mount box on top of the existing box and put a blank face place on it.  Then the plastic wire mold could come out of the raised, blank box and run to the new raised box.  The wire must always travel inside an approved box or conduit.  You can't just have wire coming out of a hole as you have described.

For the number of wires that you need to run, the current National Electric Code (NEC) guidelines say that all switch boxes need to contain a neutral.  If the existing switch box contains a neutral I would use a "4-core cable" which is sold as "14/3 w/ground" (14 gauge, three conductors) or "12/3 w/ground" (for 12 gauge - not common for lighting) to run to the new switch.  If the existing box doesn't have a neutral, I'm not sure what code and local rules would say.  I would think with such a minor change, you could just extend the wires as they currently are, and you are right that the white wire would need to be marked with black tape for the switch loop.

However, even if that is the "obvious thing to do" or "what most people would do", it might not be legal or proper, so you'll need to get clarification on that.  If you have a neutral, extend it to the new switch and you'll be ok.