"Assassination and poisoning are therefore contrary to the laws of war, and equally condemned by the law of nature and the consent of all civilized nations. The sovereign who has recourse to such execrable means should be regarded as the enemy of the human race; and the common safety of mankind calls on all nations to unite against him, and join their forces to punish him." Vattel, "The Law of Nations," p. 469 (361) (Philadelphia 1852); See also Halleck, "International Law," p. 400 (New York, 1861).
As for it applying only to the Confederacy, no, it doesn't. If Jefferson Davis had been shot in the back of the head while unarmed and watching a play with his wife, the person who did it would be an assassin.
More recently, Executive Orders 11905, 120536 and 12333 state that "No person employed by or acting on behalf of the United States Government shall engage in, or conspire to engage in, assassination." Following 9/11, the CIA was reportedly given authority by President Bush to take out terrorist leaders.