would he have done better or worse against Mayweather? Instead of having his very good jab it becomes just good, but his right hand is better.
I say he would have done worse. Right hands are essential for Floyd, but a strong jab sets up opportunities to score everything else. With a strong right jab and a lack of a strong left jab, you get what happened in round 2 against a faded Mosley. With Cotto, you get multiple opportunities to score with both hands, even if the right isn't landing with KO power. That's oversimplifying it a bit but hopefully you get what I mean.
I think the strength of his jab saved him. He used both hands pretty effectively in this fight. The real factor was that converted southpaw jab. I think he does worse.