Thus, to make a left hand ukulele, simply reverse the strings.... tune 'er up and you have a lefty uke.

As with all stringed instruments, the right and left hands do completely different movements, of roughly equal complexity. Therefore, lots of left-handed ukulele players, guitar players, violin players and the like have no difficulty adapting to playing in the traditional way (as you see above).

Some, however, prefer to re-string their ukes and play in the other direction, i.e. with the neck pointing to the right, and their right hand fingering the chords and the left hand doing the strumming. This of course means they have to translate all chord diagrams, photographs, tabulature etc. to reflect their different orientation, which probably isn't that difficult to do (especially since left-handed people are well-accustomed to living in a right-hand biased world anyways!). Because the Uke tends to be used mainly for strumming chords, a case could be made that the strumming hand might require more strength and endurance than the hand fingering the chords, making the dominant hand better-suited for the task. Not all people feel this way though.

My advice to you is to try playing in the traditional manner for awhile first, to keep life simple. If after awhile it really does feel difficult and unnatural to you, then change your orientation and compare. And please report back here with your experiences!