Aside from the stretch between the frets on longer scales, the only difference in feel for me in nut width comes with 2 and 3 finger chords when all strings are fretted on the same fret as in a D-Maj chord with fingers 1,2,3 all on top of each other (2220 in TAB).
Due to both fat fingers and hand problems now, on soprano this is nearly impossible for me to get all 3 fingers stacked inside the space between the 1st and 2nd fret without the side of my fingertip hanging over the edge of the second fret and slightly muting the string, thus I use an alternate fingering, which is like making a barre chord of the C chord shape and moving it up 2 frets, which is 2225 in tab, and only require energy being applied with 2 fingers, pointer for the barre across the 222 and pinky for the 5. Works well for me.
Longer scales may make this easier, but on concert and tenor I still use the same chord shape for a D-Maj chord.
The 1.375" is about the standard nut width for most ukes, and sometimes sopranos are narrower than that, and usually baritones are standard with the 1.5" nut width.
Smaller (thinner) fingers may allow you to stack them more easily as mentioned in the 2220 D-Maj chord, but if they are too short to reach comfortably, there are exercises you can do to extend your reach, otherwise you can look at soprano or concert ukes with a narrower nut.
You did not mention what scale length (size) uke you are playing, but if soprano is still a problem you can go smaller to sopranino, sopranissimo and piccolo ukes, all of which are shorter scale length.
Hope this helps