Here are a couple of other theories, from clickety:

....Dictionary of Word and Phrase Origins, they offer three theories. One has it that American sailors on shore leave in Yokahama, Japan visited a street named Huncho-dori, where they could get slammed in the proud Naval tradition. Apparently, Huncho-dori led directly to the docks, so the seabees knew that, no matter how bibulous they became, it was a beeline back to their ships. Therefore, the story goes, once you were on Huncho-dori, everything was hunky-dory!

Theory number two identifies a sung sung by the Christy Minstrels during the Civil War, called "Josephus Orange Blossom", and containing the line "red hot hunky-dory contraband". The tune was a big hit and the phrase became part of the popular slang of the period.

The tricky part in picking between these two theories is the dates involved. The American Civil War lasted from 1861-1865. Commodore Perry opened Japan to foreign ships in 1854. Could an esoteric bit of sailor slang have migrated back to the States so quickly at that time? If so, then both theories could be correct, with the phrase coming from sailors, and popularized by the Christy Minstrels.

Theory three is the tedious dictionary notion that the Dutch word honk, meaning "goal" or "home", is the source of the phrase. Once you reached honk, everything was hunky-dory.