I'm still struggling to see how this would be an easy way in for a beginner. To accompany Shepherd's Hey on a uke is a doddle, with the same pattern throughout (G C G D, G C D G, that's it). To play the melody, however, with those quaver runs, up to speed, isn't easy, and the sound at that pitch is quite plinky and delicate, even on a tenor. It means going very quickly up and down the fretboard, almost all on the top string. Are you sure this is going to be helpful to your friend?

But if this is really what you want, the waltz "The Man in the Moon" in G seems to tick the boxes (and isn't too fast!).

Marje