You have to remember that Hamlin was dropped not because of incompetence or animosity wit the Lincoln administration. Indeed the decision to drop him from the ticket almost never came to pass; there was a good chance that Lincoln/Hamlin would have been the ticket in 1864.
What ultimately turned the tide was the fact that Lincoln and many other leading Republicans saw the writing on the wall, and knew that the Union was headed for a massive victory. The administration elected in 1864 would preside over a period of reconciliation with the South. Hamlin was deemed too radical for this reconciliation ticket, and thus Lincoln went with Andrew Johnson, one of if not the only Southern Democrats still in Congress, in order to appeal to the soon-to-be occupied South.
If Lincoln dies before 1864, it is likely Hamlin is still the Republican nominee. The only question about the election is two-fold. One: How do the Democrats react? IOTL, they split into the War Democrats, who sided with the Lincoln/Johnson campaign and advocated for seeing the war through to its logical conclusion, and the Peace Democrats, who sided with John C Fremont and advocated for a negotiated peace with the Confederate South. Does this split still occur, or do the Democrats remain united? Two: Do we see a split in the Republican Party in 1864? Hamlin is obviously going to be the Republican nominee in some shape or form, yet he is from the radical wing of the party. Some, like William H Seward, are from a more conservative wing of the party and are thus opposed to this radical wing. Without the moderating hand of Lincoln incentivizing the radical and conservative Republicans to work together, does a conservative Republican rise up and run their own campaign in 1864, running against Hamlin and the Democratic nominee?