I refer you to SQ's website on oversized luggage. Seems like they allow musical instruments in economy class, but only if you purchase an extra seat.
"Although guitars are normally less than 7 kg (that is within the cabin weight allowance), it may be considered as oversized due to its dimensions, and may not be allowed in the cabin if no extra seat have been purchased for it. If you do not plan to purchase an extra seat, your guitar should be packed in a suitable hard case and checked in to avoid damage"
A ukulele is smaller than a guitar, so I am pretty sure it is within the dimensions for hand carry.
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