when i had an old injury on my left (fretting) hand flare up - funnily enough it was the knuckle of my ring finger, same as you! - i tried to take a break from playing but i lasted about half a day! lol! what i did, was retune the uke ever so slightly, from gcea, to gceg - open c tuning - you tune that highest sounding string down a little bit, from a to g. that means when you play the uke open, i.e. just strum and don't fret anything, you're playing a c chord. you can then bar simply, all the strings, along any one fret, just with your index finger, and you're playing - at the 2nd fret, d - at the 4th fret, e - at the 5th fret, f - at the 7th fret, g - at the 9th fret, a - at the 11th fret, b - and at the 12th fret, back to c, but an octave higher than when you play the uke open. these are all major chords. for a while, while i was playing like this, i only did songs with major chords in. this limited my song choice, but only to about half the songs ever written! lol! i actually really liked playing that way, and after my hand got better, i still used that tuning now and again. in fact i used a similar tuning literally an hour or two ago, on a song for the seasons of the ukulele here on ukulele underground, it's slightly different - as well as lowering the a down to g, i also lowered the e string down to c, to match the "proper" c string, giving me gccg, which is a kind of double power chord tuning, the chords are neither minor nor major, so if there are minor chords in the song, i can kind of cheat and play them anyway!! if you fancy checking it out the vid is here
https://www.youtube.com/watch?v=e2DJ0RlGv5Q
turning the uke round and fretting with my right hand, even with this very simple tuning, feels very very strange, i dunno if that's because i've been playing right-handed for years (guitar a long time ago, when i was a kid, and uke now), or if it's just more natural for right-handers to play the usual fret-with-the-left-hand way