Green’s Dictionary of Slang

1. higgledy-piggledy, confused, doubtful; thus on the havey-cavey, questioning, doubting.

c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Havy Cavy. Shilly Shally.
1796		Grose Classical Dict. of the Vulgar Tongue (3rd edn) n.p.: Havy Cavy. Wavering, doubtful, shilly shally.
1811		Lex. Balatronicum.
1815		B.H. Holland Iwanowna 231: Ever since then we have been, as one may say, in a havy-cavy way; neither one thing nor t’other.
1839		Grose Gloss. Provincial Words (rev. edn) 79: HAVY-CAVY, undetermined, wavering, (HABE CAVE) doubtful whether to accept or reject a thing. Nottingham.
1859		Matsell Vocabulum 41: havey cavey Wavering; doubtful.
1881		Trumble Sl. Dict. (1890).

2. duplicitious; thus play havy-cavy, to play around.

1906		H. Sitcliffe Benedick in Arcady 61: Ye don’t look the sort o’ folk, when all’s said, to go playing havy-cavy with a body’s crops.
1987		M. Kistler Mirage on the Amazon 6: I know that if there was any havy-cavy business going on in your marriage, you were the perpetrator, not my brother.
1989		(con. 1820s) Laudermilk & Hamlin Regency Companion 13: All manner of sly and havy-cavy methods were used in attempts to influence the Patronesses.