I'm awful at sports - definitely not a "natural" but I went for skiing and it was a lot of fun. I hardly fell (the first thing they teach you is the snow-plough - your safety net).
But book yourself some private lessons. That's how I did it. 1-1 with a teacher and within the first lesson, you will "go" down some small slopes but find that you are in control.
I didn't bother trying the group classes. Like I said, I'm awful at sports and group classes always meant me trying to catch up with the rest and giving my motivation and confidence the runner. So I opted for the private lessons and I must say, it is the way to go.
So No more skis on head. And Flumserberg does have some good blue runs.
Good luck
~ Nanda.