He SHOULD be best known for inventing scat singing.
Music historians really, really wanted for Louis Armstrong to the the inventor of scat singing, but there are recordings of Edwards doing it that predate Pops by a few years.
Wish I could be more helpful, aldiboronti, but I really don’t know much about the ukulele. I just like Cliff Edwards a lot. My main instrument is the saxophone, the OTHER instrument that got extremely popular in 1920s America.
My guess it that ukes were inexpensive, portable, easy to learn, and allowed the callow youths of the period to accompany their own singing as they romanced their flappers in a canoe.