You'll be able to use David Pike's utility to identify regions where you share DNA with your relativeshttp://www.math.mun.ca/~dapike/FF23utils/pair-comp.php
You will share quite a few regions with your grandparents, so this will be just a screening test to see if the results are *compatible* with the MITF hypothesis. If you test further relatives, the more distant ones will help narrow things down the most.
At a certain point, you may want to do "exome sequencing." The exome is just the small portion of your DNA (less than 2%) that codes for proteins. Sequencing (as opposed to scanning for particular rather common variants) can pick up mutations that have never been observed before. I can't post links to commercial websites, but there are some where you don't need a doctor's order.
Another alternative is to meet with a genetic counselor, who can advise you if there are clinical labs that will sequence just the MITF gene (or another plausible candidate) or research programs that might be interested in your family. If you haven't seen it already, this website has lots of links:http://ghr.nlm.nih.gov/condition/waardenburg-syndrome