You said: "I see nothing in the Constitution that prevents it (unauthorized movement of money between governmental departments).
The entire reason that Lincoln secretly ordered Seward to take money from the cash box at State was that he did not have authorized funds in the military for such an action at Charleston Harbor.
But you say he could use unauthorized money.
Who is right? You or Lincoln?
The secrecy is all in your imagination. Obviously the cabinet knew about it. Who else needed to know?