The argument can not be settled by weapons slots. Solo does not dual wield, nor does he have a hidden shotgun.
Based off of the movies, more so RotJ, Solo tends to be more SS Gunslinger. He gets back handed by a scout trooper for lack of ninja skills, and during the brawl at the shield generator bunker Solo practices some serious marksmanship with his blaster.
In the end I would have to say he is neither Gunslinger or Scoundrel, but his very own advanced class.