Green’s Dictionary of Slang

an effeminate man, one who is seen as dealing too keenly with domestic duties that are properly those of his wife.

1595		Shakespeare Romeo and Juliet IV iv: cap.: Look to the bak’d meats, good Angelica: Spare not for cost. nur.: Go, go, you cot-queane, go; Get you to bed.
1611		Middleton & Dekker The Roaring Girle III ii: I cannot abide these apron husbands; such cotqueanes!
1629		‘The Woman to the Plow’ in Ebsworth Roxburghe Ballads (1893) VII:1 186: One morning with good intent, / The Cot-quean fool did surely dream, / For he had quite forgot the cream.
1633		Ford ’Tis Pity She’s a Whore I ii: Scold like a cot-quean, that’s your profession. Thou poor shadow of a soldier.
c.1640		J. Smyth Lives Berkeleys (1883) II 372: They fell upon him with opprobrious words, of Coward, Cotquene, Milksopp [OED].
c.1698		B.E. Dict. Canting Crew n.p.: Cot for Cotquean, a Man that meddles with Womens matters.
a.1719		J. Addison in Works (1856) 37: A stateswoman is as ridiculous a creature as a cotquean; each of the sexes should keep within its bounds.
1772		Chesterfield ‘Affectation in Female Sex’ in Beauties of Chesterfield (1828) 18: They brand a man with the name of a cot-quean, if he invades a certain female detail .
1825		Hogg in Blackwood’s Mag. XVII 113: If thou’rt a Cotquean by my soul, I’ll split thy pruriginious nowl .
1854		Judge & Jury Society (Coal Hole Tavern, London) 4 July [advert] Yet the slave-dealing cotquean, may flourish and thrive, / And evading all law, he hard bargains may drive.