If I'm understanding your question correctly, you can do 1 of 3 things, as long as the guitar and ukulele are tuned the same (i.e. key of C), you can
a) Play with a capo on the first fret of your uke and play the same chords on the uke. Guitar chord = C, Ukulele chord = C
b) Transcribe the chord accordingly. For example, if the chord is C with a capo on the first fret for the guitar, the chord for the ukulele without a capo would be a C# (one half step up for the capo - each fret is a half step). Capo chord E = non capo chord F.
You also have to take into account whether the chord is major, minor, 7th, etc.
c) Pretend there is no capo and play the same chords as the guitar. It will be in a different voicing as the "original" but sometimes people don't care. Music can always be transposed into a different key to make it easier to play or make it easier to sing if it is out of someone's range.
This is probably very simplified, so I hope you understand it. Maybe someone else can explain it better.
Edit:
For example: I'm Yours by Jason Mraz
Capo on the first fret, chord Bb Major = Chord B Major without a capo.
Capo on first fret, chord F Major = Chord F# Major without capo
Capo on first fret, chord G minor = Chord G# Minor without capo
Capo on first fret, chord Eb Major = Chord E Major without capo
I originally learned this with the capo because the chords were easier to finger and I wanted to keep it in the same key so I can play along with the song. Now that I've progressed, I'm playing it without the capo and with the more difficult to finger chords (for me personally). And sometimes I played Bb, F, Gm, Eb without the capo if I can't find it just to practice the strum.
