Your willful ignorance is crazy to me. Oda chooses panelling like he decides on what characters say. You're acting that Oda didn't have Urouge call Zoro first mate out loud. Those outside the strawhats don't decide sure, Oda does. Oda hasn't made this close at all. Zoro's matchups almost always have close relationships to Luffy's, third strongest don't compare. Then there's the fact that Zoro has qualities of a captain to the point that others mistake him for one, his parallels with Rayleigh, the fact that he the only other SH with conqueror's haki. lmao why would Zoro fight King while the first mate who ranks higher than him fights the one named Queen? If it were the other way around you'd be adamant that Sanji's first mate.
Was there a chapter where those inside the crew decided on the first mate? No? Then we go by the most likely candidate, which is obviously Zoro.