Green’s Dictionary of Slang

1. a donkey.

1937–84

Partridge DSUE (1984) 545: mid-C.19–20.

2. (US, also hee-ho) loud, offensive laughter, esp. if scornful.

1884		Sporting Times 12 Jan. 5/4: The hee-haw, or the guffaw [...] may suit some people, but for brightening the world [...] give us the giggling girls.
1900		Ade More Fables in Sl. (1960) 180: They paid no Attention except to give him the Rowdy Hee-Ho when they saw him.
1948		S, Paige Pitchin’ Man 51: [T]he folk there began givin’ Bismarck the hee-haw.
1975		L. Rosten Dear ‘Herm’ 147: Which gives me a hee-haw on account he never wore a pair of boots in his life.

3. derision, nonsense.

1936		(con. 1830s–60s) ‘Miles Franklin’ All That Swagger 322: I met a man out in the Never Never – fellow with a university education – talked real hee-haw like the old parson.
1948		T. Thursday ‘Movie Stuff’ in Detective Story Apr. 🌐 The great detective always winds up behind the big hee-haw.
1962		H. Livings Nil Carborundum (1963) Act II: You’re the one that’s been giving off all the heehaw about the system.

4. in pl. the testicles.

2015

I. Welsh Decent Ride 10: A hairy ersehole wi a pair ay hee-haws dangling under it [...] just disnae dae it fir the Juice felly here.