Do I need outdoor-rated cable for an exterior receptacle?
I have heard debates on this subject.  It's very common to do just as you say, run indoor rated NM through the wall to a surface mounted exterior box.
In my opinion, when you come through the sheath, you're outdoors, and it's not compliant.  Only for inches, and I would be really surprised if it ever amounted to anything, but still not compliant.
If you want to satisfy the sticklers, you could transition from NM to UF in a box inside before the cable goes through the wall.  This also gives you some protection where the cable goes through the wall.