I agree with M. Ted and would furthur suggest that the uke sounds really good with a light tenor or alto voice because of the positioning of its register. This probably explains the popularity of Cliff Edwards and Tiny Tim. The lightness of its tone and the way its played makes it more gentle than say the tenor banjo or a Django-style guitar. The approach suggests a less frenetic and more peaceful, wistful and wafting-on-the-breeze playing which is expressed in Hawaiian music. it can swing like Ukulele Ike but remains lyrical and not as percussive as other accompanying stringed instruments.
Some of the tunes that I think it expresses best are:
"I'll See You In My Dreams"
"Dream a Little Dream of Me"
(Most any lyrical Hawaiian Hapa Haole tune)
"Ain't She Sweet"
"Song of the Islands"
"Now Is the Hour"
"Fascinatin' Rhythm" (ya' gotta hear Cliff Edwards do this)
"Honolulu Baby" (ya' gotta hear Oliver Hardy and Stan Laurel do this one)
"Has Anybody Seen My Gal"
"Moon of Manikoora"
"That's My Weakness Now"
"Ain't We Got Fun"
(Walter Donaldson tunes fit)
"I Want to Be Happy"
"When Day is Done"
"My Baby Just Cares for Me" (another Walter Donaldson)
"You're Getting To Be a Habit with Me"
"If I Had You"
"When You Wish Upon A Star" (Cliff Edwards sang this as Jiminy Cricket in Pinocchio.
The sweetness and naivete of the uke music became obscured by the popularity of the razz-a-ma-tazz of the tenor banjo and the sophistication of the guitar by the songwriters of the Thirties. Most of the Twentys songs fit well. Lyrical is the deal here in my opinion.
The George Formsby approach is different because of the banjo-uke which sounds more like a tenor banjo. Obviously, he is in a category by himself.