Green’s Dictionary of Slang

1. (US) to laugh scornfully; to smile.

1869		Man about Town 13 Nov. 77/1: For the ear distinctly tells, / ’Mid the jawing And haw-hawing, / How the side is put on by these swells.
1910		O. Johnson Varmint 158: What in blazes are you hee-hawing at?
1933		J.T. Farrell Gas-House McGinty 194: He’s one sonofabitch I’d hate to be, said Mike, as he haw-hawed.
1936		Hotspur 11 Jan. 47: Shut you mug, you hee-hawing Homer!
1999		Guardian G2 1 July 21: A man in a bad suit hee-hawing at a celebrity table with all too much to say.
2023		(con. 1962) J. Ellroy Enchanters 61: Bernie and Nat haw-hawed and watched the news.

2. in attrib. use of sense 1: affectedly upper-class.

1900		Hull Dly Mail 8 Oct. 4/3: The young gentlemen with their eye-glasses, their lisps, their hee-haw manners [...] their drawling speech.
1913		Truth (Perth) 27 Sept. 8/7: But yer toney hee-haw bounders, / Do look on such sport as ‘low’.