I know that you wouldn't necessarily jump on doing this on a guitar, but I'm wondering on a fairly inexpensive ukelele if the strings could be reversed without issue.
usually, if it is a cheap uke that does not have a compensating saddle then the answer is yes.
There is one problem to consider. All acoustic string instrument soundboards (tops) have strips of carved wood called braces (sometimes called tone bars) glued to the underside to strengthen the top but also to tune the vibrations for various pitches. The braces are never symmetrical; they are different under the side of the instrument with the lowest pitched strings compared to how the braces are configured under the other side of the instrument, with the highest pitched strings. This is a carefully-planned design to optimize the vibrations of the different pitches that the strings produce.
So, in theory, if you simply reversed the order of the strings, the sound of the instrument would change markedly and the tone quality would suffer.
Ideally you would purchase a left-handed ukelele whose soundboard would be braced in an inverse fashion to accommodate the reversed order of the strings. This is commonly available for acoustic and classical guitars, and they usually cost more, because the luthiers who build it have to do extra work that they're not accustomed to doing in large numbers.
However, an inexpensive ukelele is a simple instrument, not very sophisticated, and I doubt that you would hear much difference in the overall sound of the instrument once you reverse the strings.
You will, however, want to pay a luthier to construct an entirely new nut and a new bridge saddle if you want the instrument to play clearly and loudly and in-tune, without buzzing strings or problems with the action of the instrument.
I have revised my answer after some more experience
Original answer: I didn't even bother - I just re-tuned the strings in their original places.
Because of the 're-entrant tuning', the top and bottom strings are very close in diameter, (as are the middle 2). (G<->A are only 2 semitones apart, and C<->E are only 4 semitones apart)
It seemed to work fine, but having said that I was a complete beginner and I switched to right-handed after a month (I realised I find it fine playing righty).
EDIT: Having played righty for a few months, I tried re-tuning to lefty again (without switching strings), and it sounded wrong - and felt very wrong. So, I switched strings and it sounds great.
Just don't take all strings off at once (switch inners together, and outers together), and you should be all good. I didn't have any issues with slot width or anything.