Send it to the dry cleaner. Tell them why you want them to Dry Clean it. They may make you sign a waiver. When you get the fabric back make sure you wash it to remove the chemicals from the cleaning.
The fabric is gorgeous! Are you really sure you want to dull it? It must have called to you, even though it is shiny. When it is made up it won't be as 'in your face' glittery.