As you go along, you will find that many very good ukulele players have either small hands, medium hands, or large hands. However, none of these hand sizes stop them from being very good. Neither does their choice of instrument size depend on the size of their mitts. Not to mention the "G"-word here too often, but there are some terrific female guitar players out there who do not have huge shovel-like hands but at the same time, play a full-size guitar.
Try some stretching, invest time and effort in the instrument you love before looking for an easy way out. Next, you play a soprano and find it is actually hard to play way up the neck because there is now too little space. Now, you can stretch your grip through practice and exercises, but it is harder to cram you fingers into space that is not there. Although in all fairness, again the size of a soprano is not an absolute factor in playability at all. Practice is much more important.
Now remember, what is written above is all bluff and knee-jerk theorization, and you may very well encounter hard to reach arrangements. Warm up your fingers, stretch every time you play, try the hard part fifty times, come back and repeat the next day.
To comfort you: I have respectable hands that make a room go dark if I spread them, however I cannot yet reach some of the more intricate chords. It's not your hands.
Good luck!