He was promoting it. If he didn't give a care one way or the other, what point to putting it in his inaugural address? Why sign the letters going out to the Governors? The President plays no role in constitutional amendments. Adding his signature notifies the governors that this amendment has his support.
only in your mind
text of Lincoln’s cover letter
“I transmit an authenticated copy of a joint resolution to amend the Constitution of the United States adopted by Congress and approved on the 2nd of March 1861 by James Buchanan, President.”
A copy of the amendment and it’s cover letter were sent to all state governors, including those governors of states that had seceded from the Union.