Green’s Dictionary of Slang

1. a straw hat; also attrib., straw-hat wearing.

1899		H. Lawson ‘If I could paint’ in Roderick (1972) II 39: A boarding-house keeper, with two or three [...] straw-hatted, cigarette-smoking sons [...] I’d like to paint her and the children – and the ‘nan-nan’ sons.
1900–10		Stephens & O’Brien Materials for a Dict. of Aus. Sl. [unpub. ms.] 104: Nan-nan A straw hat for men’s wear: by transference, to the gangs of youths who affect these hats [...] They are well known in Sydney as the ‘Nan-nan or Straw-hat’ push.
1904		Sydney Sportsman (Surry Hills, NSW) 23 Nov. 3/4: [cartoon caption] The Bloke with the Nan-Nan.
1914		Sport (Adelaide) 26 June 3/7: A Johnnie in a nan-nan hat / Then raised a goatish laugh .
1941		Baker Popular Dict. Aus. Sl.

2. a dandy, also attrib.

1899		W.T. Goodge Hits! Skits! and Jingles! 39: Two little dudes of the nan-nan style / Bent on captivation.
1905		Sydney Sportsman (Surrey Hills, NSW) 9 Aug. 5/3: The nan-nan heroes from John Bull’s Land are inclined to be equally contemptuous, and talk through their neck as absurdly as the Yanks through their nasal organ.