I turn the blade with my thumb and forefinger. I don't "lock" my wrist, but I don't use it to turn the razor. Some reasons I avoid turning the razor with my wrist and use my fingers instead are:

1. I find I can get longer strokes by using the fingers instead of the wrist. Longer strokes allow me to get
more effect out of each stroke.

2. When I use the fingers only, I find it easier to get a repetitive stroke and keep the blade flat on the strop.

3. Using the fingers eliminates any variance in pressure that using the wrist may place on the strop.

4. I believe using the wrist repetitively will eventually inflame the muscles, ligaments and tendons used in turning the wrist that way.

If you get good results using the wrist, that's fine. The question, though, is: Would you get better results using the fingers only?