You can produce a Hawaiian tune on a ukulele. You just have to use an alternative tuning on either a soprano or concert ukulele. Original Hawaiian ukuleles were most often tuned ADF#B.
With today’s larger ukuleles if you tune a soprano or concert ukulele to A4-D4-F#4-B4, this slightly higher key will make a brighter, clearer tone and give the ukulele a more traditional Hawaiian sound. You would likely not want to try a Hawaiian tune on a tenor or baritone ukulele.