Green’s Dictionary of Slang

swat n.¹

(US) a heavy blow; also in fig. use.

1905		‘Central Connecticut Word-List’ in DN III:i 22: swat, n. A knock.
1908		H. Green Maison De Shine 197: She swatted Mr. de Shine, and when the Property Man protested he got a swat for himself.
1910		H. Green ‘At the Actors’ Boarding House’ in Galena Eve. Times (KS) 10 June 4/3: Ef I’d been herI’d gave him one strong swat in the jawr.
1920		Ade Hand-made Fables 65: It was Our Hero who delivered the grand Coup de Swat to the Gin Palaces.
1947		F. Brown Fabulous Clipjoint (1949) 188: Like the swat between the eyes you gave Bassett telling him where the Waupaca money is.
1955		R. Graziano Somebody Up There Likes Me (1956) 255: He would give me a big swat across the can.
1960		E. De Roo Big Rumble 73: There was the anticipation of the swats to come. Two guys took off their garrison belts.
1971		B. Moyers Listening to America 203: Give one of those kids a swat on the chops.
1983		S. King Christine 77: ‘Go back to bed, little one,’ Dad said, and gave her butt a light swat.

In phrases

cut a swat with (v.)

(US black) to make a success [play on hit n. (1b)].

1938

E. Freeman ‘The Whirling Hub’ in Afro-American 6 Aug. 18/3: Those Hebrew gals are cutting a big swat with the boys of Everett.