It seems to me the problem is that the written guitar chord on the sheet music would be in the wrong key for the music, should I play it on my uke. Since posting this and having a look around and received personal emails, I need to move the chords five frets up (?) then I will have the correct chord. (Am I right?)
You're wrong and you're right at the same time.
Jazz chords are typically written in the correct key for the song. When I say "written," I'm talking about the actual
name of the chord. Cmaj7 or G7(b9) or whatever. That is the
same name, no matter what instrument you decide to play the chord on--guitar, uke, piano, Chapman Stick, accordion, xylophone, etc.
So if you see the chord "Cmaj7" you would play a Cmaj7 on your uke (0002 is one possible way). No transposing is required. You do
not need to change that chord to any other chord. It's still a Cmaj7 chord.
Now, because a guitar has more strings, and since those strings are tuned differently, the
way you play that chord is going to be completely different. So if you see any additional notation on your sheet music that tells you
how to play the chord (such as a chord diagram box, or written tablature), then that is for
guitar only and should be completely ignored by you, since you are not playing guitar.
It's true that there is a pitch relationship between guitar and uke. That might tempt you to try to get the ukulele chord positions by taking top four strings of a guitar chord diagram and moving it down several frets. I would recommend against this! For one, unless the chord diagram is entirely at the fifth fret or higher, you simply cannot move it down far enough. Two, you'll be missing two strings anyway, and those strings might have some important notes that you shouldn't get rid of. That is, the top four strings of a jazzy guitar chord might not effectively convey the entire chord, in the way that a proper ukulele version of the chord would.
The solution is to use a good chart of chord diagrams that is designed specifically for the ukulele. A lot of chord charts you find on the internet tend to have basic chords only. The Mel Bay ukulele chord book is nice. An there have been some interactive websites mentioned here already that will show you tons of crazy chords. Alternatively, you can learn a tiny bit of music theory and just figure out how to play all these chords on your own.
To summarize: Ignore the guitar chord diagram. Refer just to the chord name. Ignore the guitar chord diagram. If you don't now how to play the chord, look it up in a ukulele-specific reference. Ignore the guitar chord diagram.
Did I mention that you should ignore the guitar chord diagram?
JJ