That requires a WAG, but slavery was dying as an institution due to the industrial age. The South's industry, what little it had, was destroyed in warfare; mainly in Sherman's Scorched Earth campaign (now illegal by the Geneva Convention). This put them even further behind the industrialized north. To some extent, they still haven't caught up.
IMO, had Lincoln done nothing but try to maintain cordial trade relations with the South, I think that by the 1900s, slavery would have been abandoned and the nation reunited against an increasingly hostile world. Maybe WWI would have dragged on longer, so long there was no WWII, because the US didn't enter under President Wilson. There's a cascade effect to major changes in history. Change a major thing and it changes everything else.
Regardless, I think slavery was dying as the world became more civilized. Notice that it mainly exists in undeveloped countries and is illegal across the industrialized world due to the conflict between the ideals of unalienable rights and forced subservience.
I agree that slavery in the south would have been gone eventually with or without the war. I suspect though that the separated South would *still* be struggling economically today unless they had figured out another source of cheap labor, and had the technological means (brains and labor and materiel) to create manufacturing/industry. Cotton and tobacco were not sustainable to promote a thriving middle class.
