Would this be appropriate for me to do at work?

I think it's a wonderful idea. Sounds like great fun that would give everyone in the office a smile. It's also thoughtful, because people may see a lot of others getting individual gifts on that day, and even if they don't get anything from "someone special," being part of the group that received the gift might help them feel a little better. As for a second song, if they're familiar with it, I think Hugh Laurie's "Mystery" is a hoot ... you can look it up on YouTube if you don't know it. Or maybe "My Funny Valentine" for a more traditional song.