We have been making this dish, using a recipe from a cookbook we bought in Greece. I use the non-fat Greek-style yogurt.
The trick to keeping it from getting watery as it stands is to salt the cucumber after it's shredded and then squeeze it dry after it's sat for 15 minutes.
I recommend Greek yogurt as a substitute for creme fraiche...
It's usually cheaper and easier to find, it won't curdle when added to hot items such as beef stroganoff, and you can enjoy the leftover yogurt for breakfast!