I don't think it should be too much of a problem with small hands. I've got pretty small hands (smaller than Aldrine's anyway) and I can at least get them in position to mute all the strings I need to mute ... moving them around to play different notes quickly is a matter all it's own, though.
A couple tips for people starting out:
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Really reach your thumb around to get it over the fretboard. Normally when you play, the neck of your ukulele rests in the palm of your left hand. When you reach around to mute with your thumb, the neck should be resting on the lower half of your pointer finger, while it holds the note. By moving your palm out of the way, you'll have a lot more reach.
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Position your thumb a little higher than the note you want to play. If you watch the
video, Aldrine puts his finger on the bottom string (3rd fret), reaches around with his thumb and places it two frets above (5th fret) to mute the strings. For some people, placing their thumbs a few frets higher than the note will actually help them. Try your thumb in different placements, to see what's easiest for you.
Try it out and see!