Good points, everybody. I'll just add a couple of things:
It's easier to get away with ignoring the bass note in a slash chord (the "bottom" or "right side" of the slash)
when that note appears in the chord already. In those cases, you're still playing the note, but maybe not as the
lowest note. So a C/E or a C/G could just be played as a C without the song suffering too much, because a C chord already has an E and a G in it.
But when the note
isn't normally in the chord, you might want to think about adding it in, regardless of whether you add it to the bottom or not. For instance, the previous example of C/A should be played as a C chord with the A note tacked on (which is a C6, or an A-7, depending on how you look at it). A regular C will sound noticeably different.
Finally, realize that a good number of the chords most people play on the ukulele are actually "slash" chords anyway, even when the song calls for a plain-old, root-position chord. I haven't heard anyone complain yet, which goes to show you how unimportant that bottom note is on a small-range instrument like the uke.
Here are some examples of open chords you probably play all the time, along with what they "really" are (assuming a standard, high-G uke):
F (2010) = F/C
G (0232) = G/D
A (2100) = A/C#
Bb (3211) = Bb/D
E7 (1202) = E7/D
"Hawaiian" D7 (2020) = F#dim/C
JJ