unbent or frozen right wrist merely means NO HORIZONTAL MOVEMENT. It is not a tension thing to maintain the bend. It is not stiff only limited in motion.
After swivel, the right wrist will straighten somewhat, more with Swingers and LESS with hitters, due to the power of the driving right arm to extension (extension action or the left arm) or throwout of the left wrist cause by CF for a swinger.
Both are non-voluntary actions. Someone with little or no power could keep the bend in either stroke, like a chip or pitch.