Stock prices did go down. As with today's Brexit, uncertainty hurts the stock market. I don't know abut the "wave of bankruptcies," though. So far, we just have the word of some very anti-Lincoln papers for that. Just as with Brexit, newspapers added what they expected would happen to their reports of what was actually happening. I'd like to see some real evidence, but I suspect businessmen were watching and waiting and hoping to weather the storm and most of them did.
Reports on the Confederate embargo of cotton exports are unclear as to how much Confederates actually held back from export, how much they burned, and how much eventually found its way to foreign markets (including Northern US) by more circuitous routes.
Reports do say there were great surplus stocks built up in Northern and European warehouses by 1861, and so there was little real "crunch" felt until 1862, by which time alternate sources (i.e., India, Egypt) were beginning to come on line.
It's a little like an OPEC oil embargo today -- yes, it would hurt some short-term, but soon other sources (i.e., fracking) would come into production, users would shift to alternate energies (i.e., natural gas), and life would go on...