A false analogy leading to mistaken conclusion.
That's because in, let's say, March 1861, the new Confederacy was outnumbered by the Union voters, 10 to 1, meaning the potential drop in demand for US imports was just 10%.
Yes, the loss of cotton exports could reduce total United States exports, theoretically, by 50%, but New York would see, at most 1/3 of that, since the vast majority of US cotton shipped directly from Southern cities like New Orleans & Mobile.
But what about all those other "Southern products"?
Well, the reduction in all so-called "Southern products" in 1861 was $163 million vs. 1860, but, $160 million of that was just cotton!
Non-cotton "Southern products" net-net fell only $3 million.
And outside the South, Union exports rose $61 million in 1861.
Point is: even as early as 1861 the Union in general and New York specifically was quickly adjusting and adapting to the loss of Confederate cotton.
So there's no reason to think it would have ever permanently crippled a city as dynamic as New York.
DiogenesLamp: "Slavery was eventually going to die of natural causes, but the remnants of the North's war on the South, and the precedents it established, have lingered much longer than slavery ever would have."
No, that's totally misconceived.
So see why, suppose a historical hypothetical: that secession was declared in 1861 after the reelection of President Buchanan, and suppose Democrat Buchanan had allowed the Confederacy to "depart in peace" taking with it what they wanted, i.e., Maryland, Kentucky, Missouri, Oklahoma, New Mexico, Arizona & even California.
Then let's suppose that Confederate military prowess was spent on, not fighting the Union, but on what were then called "filibusters" -- adventures in the Caribbean, Central & South America to establish new lands for American slavery.
And let's assume that with Confederate government backing, these new "filibusters" were highly successful.
Now look at hypothetical maps of the North America and the world.:
Given this 19th century victory of slavery and empires, what conceivable pressures -- economic, social, political, etc. pressures -- would ever force nations to abolition?
Why do you show so much British encroachment into the upper eastern and western lands of the USA in this scenario?