Thanks for the suggestions, so far.
I had forgotten Iris, but I have it. I'm not sure that it would really work for a wedding, and a real obstacle is that it is 4:50 long!
I LOVE dancing to What's New Pussycat - but it is hardly 'modern', as someone said. Delilah is another Tom Jones VW'able track, but not really suitable.
I quite like Enya's Caribbean Blue, and Patrizio Buane's 'Have You Ever Really Loved a Woman' goes at a very moderate tempo, but would suit inexperienced dancers for that very reason.
Any other ideas will be very welcome.