Conan was a very decent thief in Tower of the Elephant, dodging tigers(well, almost) and guards, climbing the tower, etc. After that he apparently did a lot more gigs as well(if comics are to be believed). Not to mention, he worked as a corsair for a decade, which wasn't mere headbashing. Conan has a working knowledge of stealth, rogue's craft and general swashbucklery, and I'd say he'd be at least a level 4 rogue. I'd like to say 6 or 7, but that would start to outweight the barbarian aspect. The main point is that for a time his...profession wasn't a "barbarian", which is a reason to enough to not make him a pure one.
As for being unarmored, well it depends. In Phoenix in the Sword, Conan wore armor and he's used stuff like padded leather before, it's just that the standard Cimmerian is the Red Nails-Conan who fought naked waist up. Sort of a misconception really, Conan probably wasn't stupid enough to gear up like that when the job was known to include battles and raids and not just tombraiding in the tropic, for example, it's not a huge stretch of mind to imagine him wearing armor when he worked as a mercenary in the steppe or a caravan guard somewhere else.