Many ukulele groups have published their own songbooks. Here are the links to a few…
Here's a large list of songbooks courtesy of People of Lewisham's Ukulele Club in the U.K.
"A fake book is a collection of musical lead sheets intended to help a performer quickly learn new songs. Each song in a fake book contains the melody line, basic chords, and lyrics - the minimal information needed by a musician to make an impromptu arrangement of a song, or "fake it."
The fake book is a central part of the culture of playing music in public, particularly in jazz, where improvisation is particularly valued. Fake books are not intended for novices: the reader must follow and interpret the scant notation, and generally needs to have thorough familiarity with chords and sheet music. However, fake books can be an avenue to playing songs quickly; a few chords and a one-note melody line can allow even an amateur to play a passable version of any song with relative ease. Despite the name, fake books are often unbound, consisting of a thick, loose stack of sheets. " (https://archive.org/details/fakebooks%26tab=collection?tab=about)
The Toronto Public Library has many Fake Books which you can borrow (you need a TPL Library card). Click below to see TPL's collection of Fake Books.