This can be a somewhat simple solution... if you know the principles behind transposing.
Find all the chords you use in the key you're most comfortable with and list them (alphabetically might help
unless you need to see them in some other kind of relation to each other, like C, Am, F, G7)
once you get your 'full' list of chords, using the principles of transposing, or a chart, simply find the corresponding
chords in your next favorite key, then the next and so on.
If the 'song' you've selected uses a lot of chords, then when you're done with this project you'll be able to play
that song in each of the keys for which you've created a corresponding list.
In a sense that's what I did for the Ukulele Boot Camp in terms of the exercises for each key. Beginning with the
key of C all I did for the subsequent keys was to transpose the chords in the key of C to the keys of F, G, A, and D.
You could also add Bb and E if you like. I didn't because there doesn't seem to be many ukulele songs in those 2 keys.
Enjoy and keep uke'in'
(PS the Boot Camp link is below my signature)
PPS all that being said, a fuller Transposing Chart will show the chords and keys in relation to each other in an alphabetical arrangement.