Lets say that the initial secession fever that grips the deep south after Lincoln's election isn't as strong and only South Carolina, and maybe one or two other states, and Georgia isn't one of them, have actually seceeded by the time Lincoln takes over.
My guess is in this scenario Lincoln will take a more Seward like approach and hope to wage an undeclared economic war, evacuating Fort Sumter so as not to reignite Southern passions, and just wait out events in the hope that unionists gains strength, if not at first in South Carolina, than for sure in the other seceeded states. With every passing day that goes by without some nefarious act on his part, Southern unionists might very well be strengthened and the gloom and doom southern extremists who stampeded the whole lower south in OTL will lose credibility. The only immediate down size that I can see for this approach from Lincoln's standpoint is that with each passing day of inactivity this mini-secession will grow more real, and take on a de facto sense of legality, if the unionists in these states can't take the political initiative.