This link claims that one cannot be sure of origin of this phrase. Three explanations are given here, but they are not very convincing (I am not a native speaker).
In one of our newspapers, someone gives an explanation. Apparently,
Duke of Wellington, the man who defeated Napoleon Bonaparte in the Battle of Waterloo in 1815, though quite the ladies man, wasn’t really much to look at. The most prominent feature of his not-so-handsome face was his rather long nose. The officers and the men who served beneath him began to affectionately refer to any nose which was unusually long as ‘duke’. With the passage of time, this word began to be used to refer to any nose; of whatever size. Since human fists are notorious to be employed in fights to put a ‘duke’ out of joints, fists began to be called ‘duke buster’. Soon, the word ‘buster’ was dropped, and everyone started referring to fists as ‘dukes’.
This sounds like a great story, but he did not cite any references. Since this explanation is so very different from many others available on-line, I wonder if there is some reliable reference in support of his claim.