General sense of squeezing or twisting:
* Squeeze
* Twist
* Press
* Compress
* Pinch
* Torture (figurative)
Specifically referring to wringing hands in distress:
* Clutch
* Grip
* Grasp
* Twiddle
* Fidget
Figuratively, meaning to extract or obtain something with effort:
* Extract
* Force
* Elicit
* Draw out
* Coax
* Convince
To get the most accurate synonym, please provide the sentence or phrase where "wring" is used.