Nothing at all. But of course shipments from the North to Mexico would have been similarly interrupted, and you are invited to imagine how long it would have been until other western territories would have chosen to throw their lot in as states of the Confederacy, rather than seek union with the USA.
Similarly, shipments from Central America would have had to travel by sea rather than by the IRCA railroads that later came into being as a result of Yankee development, and the banannas and other exports would have likely found waiting markets in the southland rather than in longer voyages to the north in those pre-mechanical refrigeration days. The exchange of southern-produced light industrial goods in exchange would have further developed such trade and stimulated southern industrial capacity, and it's interesting to speculate as to whether the Panama Canal would ever have come into existance at all.
I believe it was Winston Churchill's article on a fictional Confederate victory in the War of Northern Dominance that World War I might thereby have also been averted. Happy thought, and too bad that that didn't work out that way.
-archy-/-
We had a lot of trade with Mexico did we? Enough to justify a rail link? Of course not, and our transcontinental railroads all ran east-west, not north south for that very reason. There wasn't enough trade with Mexico and there sure weren't many Mexican railroads to tie in to. No railroads ran the length of Mexico to tranship goods from Central America so you were back to ships for that transportation as well. Trade with those regions, such as it was, would have remained pretty much undisturbed. As for the 'southern produced light industrial goods', well there weren't any.
"War of Northern Dominance", eh? That's a new one. Never heard Jeff Davis's War called that before. But, I digress. I don't think that a southern victory would have prevented WWI, it probably meant that the North and South probably would have fought on opposite sides. A southern victory would have left hard feelings and an armed border between the two countries. If the confederacy cozied up to Great Britain then it's possible that the U.S. would have looked for allies among the other European powers, Germany or Russia. Squabbles between the European powers, like the Franco-Prussian War could have spilled over into North America. Instead of preventing WWI, a southern victory might have brought it about sooner.