Green’s Dictionary of Slang

1. a stupid person, a person who is conventional.

1936		Reading Times (PA) 29 May 4/8: ‘Ickies,’ I’m told, wouldn’t appreciate [Louis] Armstrong and [Stuff] Smith’s incomparable style, but ‘jitterbugs’ are greatly affected.
1937		Metronome Mar. 30: Once again I’d like to rise up in arms against the ‘unseen horde’ of ickies who under the guise of posing as musicians and ‘heppers’ persist in burdening us readers.
1938		Pic (N.Y.) Mar. 9: an icky. — a phony, corny guy. The kind of college freshman who asks the leader to ‘please play Tiger Rag’ when it’s just been played.
1944		C. Himes ‘Let Me at the Enemy’ in Coll. Stories (1990) 37: This George Brown was strictly an icky.
1955		Shapiro & Hentoff Hear Me Talking to Ya 189: I [...] grow far more excited than any of the most obnoxious ickies.

2. a member of the upper classes.

1953

L. Durst Jives of Dr. Hepcat (1989) 1: Let all the ickies drape in shape and fall from the pad hip to the tip and most mad.