Honestly Oda is inconsistent with the concept of swordsman, but after Mihawk taught Zoro haki during the timeskip and Zoro unlocked acoc ( using his swords), how can someone says that haki is not important for a swordsman? According to some logic Zoro will turn off his conquerors haki against Mihawk (because it's not a swordskill), only armament and observation haki can be used ( definitely swordskills )