I have no idea of how much cotton was shipped out of New Orleans and I doubt anyone does.
It just doesn’t make sense anyway. New Orleans was a huge distance to travel from Europe.
From wackypedia:
Antebellum New Orleans was the commercial heart of the Deep South, with cotton comprising fully half of the estimated $156,000,000 (in 1857 dollars) exports, followed by tobacco and sugar. Over half of all the cotton grown in the entire United States passed through the port of New Orleans (1.4 million bales), a full three times more than at the second leading port of Mobile, Alabama. The city also boasted a number of Federal buildings, including the New Orleans Mint (a branch of the United States Mint) and the U.S. Customs House.[5]