Is the body of the ukulele structured for right-handed people? Can left-handed people play the ukulele without discomfort?
It depends on how. the body of your ukulele is shaped. Most ukuleles look like smaller accoustic guitars, ie. symmetrical, so no problem there. Some custom ukuleles would have this problem, but in general no.
Additionally, if you want to switch the strings, the tensions are so similar that you don't have to worry about breaking the ukulele when restringing for lefty playing. Of course, one could simply hold it like a lefty and read chord diagrams backwards (I've heard imagining seeing through the neck to get to the fretboard helps, but I'm not lefty, so I don't know).
The ukulele is one of the easiest instruments to adapt for left-handers.
Since the back of most ukes are symmetrical, it won't make any difference whether it's played with the neck facing left or right. Unlike some electric guitars, which are built handed - but that doesn't stop some players! Even the cutaways don't cause too much grief (double, obviously!) The strings will be in the 'wrong' places if it's just turned round, but even that isn't a huge problem - unless you've already learned the shapes - albeit with the wrong hand now! Highly unlikely. And swapping strings round is no big deal.
A lot of lefties on all kinds of instruments will opt for a right-handed approach, due to several factors - better choice of less expensive models, ability to play someone else's instrument, the fact that one's dominant hand (mainly fingers) is /are playing the more intricate stuff.
Bearing that in mind, I've taught far more lefties to play right (on guitar and bass mainly), than I have taught lefties left-handed. It's not a problem either way for me, but weighing up pros and cons often tips the balance. There's always the one or two who are entrenched in lefthandedness, and I respect that.
So basic answer is no difference, but why?!