Green’s Dictionary of Slang

exchanging one thing for another, bartering.

1695		J. Edwards Authority Old and New Testament III 231: Swapping or bartering of one thing for another [OED].
a.1739		C. Jarvis (trans.) Don Quixote III vii (1742) I 110: The laws of chivalry [...] do not extend to the swapping of one ass for another .
1825		J. Neal Brother Jonathan I 23: After having grown old in the ways of the world [...] hypocrisy, ‘swapping’, trading, and evil speaking.
1885		Bulletin (Sydney) 3 Oct. 22/3: Then the committee conceived the brilliant idea of ‘swopping’ books with the Alexandra Free Library Committee.