The OED quotes a first ref dating only from the 1890s and has less etymology than the AHD entry:

Schmuck

slang.


Also schmock (SmQk), shmock, shmuck. [Yiddish; originally a taboo-word meaning ‘penis’.]
A contemptible or objectionable person, an idiot. Hence "schmucky a., objectionable, obnoxious.

1892 I. Zangwill Childr. of Ghetto II. i. xvi. 45 Becky's private refusal to entertain the addresses of such a Shmuck.