It might work if you just made him sing the first few phrases and then changed scenes, coming back to him later. It might be best not to cut to another scene, but just have him stop after the first three sentences or so and then have Palpy deliver his lines, but I'd have to see it to decide for sure. I'm not sure how good the idea is anyway, but it came to me when I was listening to the song so I figured I would post it and let others decide...
This could be repeated again in Episode V when the Emperor speaks to Vader via hologram, with the emperor singing this time.