I’ve never heard that song before but I love to watch well-choreographed swing dancing! I danced (took for many many years and my mother was a dance teacher) and love swing dancing but have to say…I’m more of a Fred n Ginger type of couples dancing fan..and theirs was a cross imho between swing and waltzing.
Have you checked out some of his old movies for inspiration? I think you two would be so graceful dancing and if that song speaks to your hearts, go for it!
Not sure how it will work for swing dancing, but just wanted to say that I love that song, too! I think that Madeleine Peyroux did a cover of it that might be a little more dance/crowd-friendly. Pretty jazzy.
As a former swing dancer and a fan of Leonard Cohen, I can tell you that I think this would work. Mind you, I would not call it a swing song and it was never played at swing dances that I went to. But I just listened to it again and it’s a good tempo. If you are planning on taking lessons (there are some EXCELLENT teachers/dancers in DC), just bring the song and the teacher will tell you what he/she thinks. Good luck.