Your claim would have Lincoln as Davis' puppet. I think he was not. I think Davis was his.
This claim conforms to the old explanation that clever Lincoln somehow "tricked" simple Davis into starting war at Fort Sumter.
One problem with it is that Davis himself never admitted such a thing, and indeed his own words long before Fort Sumter tell us he intended to start war at both Forts Sumter and Pickens.
Another is that by very far, Davis was the more highly trained and experienced political & military leader, a West Pointer, war veteran with decades of political experience by contrast with whom Lincoln was a simple & poor country bumpkin.
I think it's unfair to call either the other's "puppet".