I have always thought of the "Donkey",at least in this instance,as being the capstan,whereon the fiddler or other musician would sit whilst a capstan shanty was being sung,hence "riding on a donkey"--I am prepared to give it some credence,anyway ! Simple & logical.
    Whilst serving before the mast Ha Haargh Jim lad,my fellow Lowest-Forms-of-Human-Life and I were wont to refer to our Chinese colony as "Honky Fid". A "Kong" was four of a kind in "Mah Jong"---times change !!