The survey of College Words and Phrases by Eugene H. Babbitt published in 1900 cites Elmira College, NY as the source of the word 'waddy' with the definition "Queer and unattractive" and the secondary definition "Mean and contemptible." The word does not appear in William Clark Gore's study of Student Slang in 1895 so if it emerged into common use it was probably during the course of the late 1890s.
I doubt there's any easy way to determine exactly how a particular slang word came about but the word "waddy" was in common use to describe primitive club-like weapons used in Australia from the late 1800s onward and came to be synonymous with basically any sort of stick that was used as a weapon.
Waddy is also a surname so it's entirely possible that some particularly hideous professor or student at Elmira college bequeathed the term with its meaning.