G# is the same as Ab. (So Ab minor would be the same as G# minor.) I think the simplest way to play G# is to make the G chord shape using your middle, ring and pinkie fingers, move the shape up (cloder to the body of the ukulele) one fret, while using your index finger to barre the fret closest to the nut. In other words, G# is just G up one half-step (i.e., up one fret).
he he...or you can play the laaaaaazy way (like me) and play the G shape up one fret and not strum the 1st string. Or, on a soprano you can let your thumb hang over and hit the top string 1st fret while holding that standard shape, but that is a little more difficult on the longer scaled ukes.
Here are the 12 notes and their names. 5 have two names and the chord shapes are the same for each combo IE A# and Bb are the same chord, etc for the other 4 combos.
Notes C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B