I wouldn't advise dying a dry-clean only article because dying is a water based activity, which the garment isn't really made up to survive. You can buy dyes for silk though but I'd be more worried about washing the dress - if it is lined then you may find that the two different sections react to the water differently and you'd probably lose the beautiful shape.
Just a thought, if you are any good at dressmaking, you could add a holey, lacy or really fine sheer fabric (in a different colour) to the dress to transform the overall colour.
Here are a couple of pictures of what I mean:-
http://www.styleplus.ie/images/FiorellaLaceGow n.jpg
http://www.casalena.co.uk/images/K004.jpg