I love playing 'The Only Exception' on ukulele and have a simple no-capo way that works great for singers who want a mellow, singable key. If you want to keep it easy, play it in the key of C using familiar shapes: C (0003), G (0232), Am (2000), and F (2010). Those four chords let you cover the whole song without juggling weird voicings, and the progression sits nicely under most voices.
Start with this basic roadmap: Verse = C — G — Am — F (repeat), Pre-chorus = Am — F — C — G, Chorus = C — G — Am — F (you can add an Em (0432) or D (2220) for color if you like). For the bridge, try Am — Em — F — G and then return to the chorus progression. This structure keeps the emotional lift where the original does while staying totally uke-friendly.
For strumming, I like a relaxed D D U U D U (down, down, up, up, down, up) at a slow-medium tempo. If you prefer picking, an arpeggio like 4-3-2-1, 4-3-2-1 (string numbers G-C-E-A) on each chord sounds intimate and suits the song's wistful mood. Work on smooth chord changes between C → G → Am → F: practice shifting your ring finger from C to F and your index/middle fingers for G and Am so transitions are fluid. Play around with dynamics: keep verses soft, open up on the choruses. I always end a run-through by singing the last line softly and letting the F ring — it feels simple but satisfying.