Here is how I would stat Conan.
Race: Human Variant (Cimmerian)
Class/Level: Barbarian 2 Fighter 11 (Battlemaster)
Str 18 (16 base +1 Racial +1 feat: tavern Brawler)
Dex 16 (15 Base +1 ASI)
Con 20 (18 Base +1 Racial +1 ASI)
Int 13
Wis 16 (15 Base +1 Feat: Resilient)
Cha 14
Save Proficiencies: Str, Con, Wis
Feats: Lvl 1 Tavern Brawler, Ftr Lvl 4 Resilient, Ftr Lvl 6 Mobile, Ftr Lvl 8 ASI
Battlemaster Maneuvers: Menacing Attack, Sweeping Attack, Riposte ( Riposte not being a fancy move but an almost animalistic lunge under an oponents missed attack that makes them look rigid by comparison.)
I lean away from giving a twenty strength. His endurance and durability were constant. One thing I see many builds overlook was his Will. He had an iron will and it would take wisdom to rule. I would say if anything should change it would be strength.
I would not give him proficiency in social skills. If he intimidates someone I would assume they are not impressed with his words but rational in their fear of disembowelment. Being in the same room with Conan would be like being in the same room as a lion. You can be part of the pride or you can be lunch.