It’s surprisingly easy to play complex harmonies on a ukulele, in many cases because the first and fourth strings (A and G) are only one tone apart.
One of my earliest posts here on the GRÜBS blog, about the process of writing “Sweet Rebecca”, alluded to this. The chords in that song are all jazzy ones with complex names, yet most of them are individually easy to play, and in most cases changing from one chord to the next is also pretty easy. Here are diagrams for a few of them. [G major 7: barre across the first three strings at the second fret; C major 7: first string, second fret, B minor 7: barre across all four strings at the second fret; E-flat major 6: barre across all four srings at the third fret]
And here is an article by James Hill illustrating this point further: http://www.ukuleleyes.com/issues/vol7/no3/pedagogy-corner.htm. He recommends a three-finger “Bb6” voicing, which is easier to play than the regular four-finger Bb chord, even though it sounds more sophisticated. Another kind of Bb chord that’s a little easier to play than the standard one is the three-finger Bbmaj7 [first fret on the second string, second fret on the third string, and third fret on the fourth string].
Recently I was working on a new GRÜBS arrangement of a popular song. Although I knew I would probably end up playing bass, as usual, I wanted to record a demo of my arrangement for the rest of the band, so I was figuring out how to play all the ukulele chords. The last three chords of the chorus were B7, E7, and A. For me, that progression was hard to play quickly, so I decided to look for an alternative (ideally, something that would also help put an original spin on the arrangement).
One option was a tritone substitution, which is a very clever thing jazz musicians do sometimes, and which I had learned about decades ago in college, but which I’d never really done before in real life. As the phrase “tritone substitution” implies, I eliminated the E(7) chord and substituted a Bb(maj7) chord (because Bb is three whole tones – i.e. a tritone – away from E).
Then I noticed something truly grand.
The new progression was B7 – Bbmaj7 – A, which I could play by just sliding my left-hand fingers down one fret for each chord!
I’ve posted a few other recommendations for “cheat” (i.e. substitution) chords here and here; as I’ve said before, these cheat chords will not always work for every song in every style, but you may discover others through experimentation; listening is always the key, because music exists in your ears, not on paper …