I recently read a biography of Leonard Cohen (I'm Your Man, Sylvie Simmons) which mentioned — off-handedly — that he plays uke. So it seemed a charming match.
I'm currently reading The Holy or the Broken by Alan Light, which is an exhaustive study of the growing popularity of this song. Aside from a discussion of record sales — a necessary evil — he talks about how each singer's interpretation brings something new to the song.
My interpretation, as is often the case, is a syncretic blend of other interpretations that have spoken to me. My aim is mix moments of innocence (an element of the Buckley interpretation, according to Light) with moments experience (Cohen's original and John Cage's cover).