I found an 1889 example of honky-tonk: some 35 years earlier than the OED's 1924 honky-tonk, and some five years before their 1894 honk-a-tonk.
The Fort Worth Daily Gazette (Fort Worth, Tex.), of January 24, 1889:
A petition to the council is being circulated for signatures, asking that the Honky Tonk theater on Main street be reopened.
I found a good definition in The Iola Register (Iola, Kan.), June 23, 1893:
When a particularly vicious and low grade theater opens up in an Oklaholma town they call it a "honky-tonk." The name didn't just "come from" anything; it just growed.
The Sun (New York [N.Y.]), November 26, 1897:
BURNED DOWN THE "HONKY TONK"
Louisiana "regulators" break up a Vicious
Resort and Shoot a Man.
NEW ORLEANS, Nov. 25.-Last night a party of regulators, about thirty-five in number, appeared at the Gramercy sugar refinery, in St. James parish, to break up a "Honky Tonk" there, where gambling, drinking, and all manner of vice prevailed. The regulators severely whipped the eight negro women in the "Honky Tonk" as well as the men they found there. Some of the negroes ran under the house to escape the beating. The building was set on fire and burned to the ground. Fears are entertained that some of the negroes were burned to death under it.
Oscar Dressner, a white storekeeper, who lived near the "Honky Tonk," came out to see what the regulators were doing, and they, fearing that he would recognize them, opened fire on him. He received four dangerous wounds in the back. Ho was brought to the Turo Infirmiry in New Orleans for treatment. He says he can Identify five of the men engaged In the
More: 1898, 1898, 1898, 1898, 1898, 1899, 1899