The actual Japanese word used by Urouge is 2番手 which doesn't mean vice captain/first mate but rougly translates to 2nd in place, he is basing this off of the only piece of information he can which is Zoros bounty (similar to Black Maria referring to Sanji as the 2nd in place bounty wise), that was in fact the 2nd highest. Rayleigh on the other hand is called 副船長 which does mean vice captain, as well as 右腕 which means "right arm", note that these words have never been used to describe Zoro in any of the Japanese sources.
In fact Oda himself confirmed that Zoro wasn't the first mate in an SBS where he was asked about the "numbers 2s" color spread where he says, "That cover, huh? Similar to Zoro, not all of those characters have the title of first mate. I selected the No. 2s as I saw fit. Usually, Shachi and Penguin are more dependable, but those two—who have seen Bepo's Sulong form—are no match for Bepo in terms of fighting power...! I acknowledge him." Now Oda in SBS volume 73 refers to both Zoro and Sanji as the "wings", he later on put this in the manga through Robin( same kanji). That statement stands as the only somewhat official special title that Zoro holds which separates him from the rest of the crew, besides the " combatant" role that he is always listed as holding. Now I do see Zoro as Luffys "right hand man" as I see Sanji as the "left" but this is purely based off of the wings title(alongside general portrayal) and not because the word is officially used by Oda for Zoro or Sanji.