When I wanted to dye my daughter's white communion shoes (same sort of thing, white satin), the chap in the shop said to me, don't waste your money having it done professionally - use food colouring, just as good and you can make it up in the colour you want. I mixed red and blue bog-standard-bought-at-Tesco's-on-the-baking-aisle food colouring, tested it on some white fabric first to make sure the colour was right and it was very successful (hands were a bit purple for a while, but there you are!).