I read a great tip here - rub your fingers on an alum block to improve grip!
As well as making it easier to stretch your face I think you are less likely to lose grip on the razor.
Alternatively, use a washcloth on your hand to stretch your face, or simply wet your fingers and rub away remaining lather from where you want to grip.
I use both hands to hold the razor, it just seems the natural way to reach some areas. But I think you should do whatever feels right. Maybe force yourself to swap hands occasionally on an easy area so you develop the skill, you might then find yourself swapping hands instinctively later.