Lincoln was a politician, I thik he could have managed. Remember, he was very popular. If there is an attempt, but the bullet misses, I think he's even more popular, and the Radical Republicans won't give him lots of trouble.
I think the 14th and 15th Amendments, might be one way in which we see Lincoln bend to suit them. He was, as was stated, more concerned about the Union, and preserving it, then he'd worry about the peace later. It sounds reasonable that he'd hold his opinion on Amendments 14 7 15 (13 was a given, IMO) and when the Radicals pressed him on other issues, give in on those two in a spirit of compromise.
Not only that, but if Lincoln's impeached, they get a Southern Democrat in Johnson. I doubt the Radicals would want to with that staring them in the face.
Question - if Lincoln is kinder to the South, does that lessen tensions some and allow for things to go a little smoother for my idea of baseball integrating early? Perhaps this fictional player who survives the Civil War somehow manages to put in play things that cause the guard to be there to stop Booth that nice at the theater?