I'm afraid you are mistaken, the watch relies on your arm free swinging.
You can try to calibrate it using a walk and run workout to improve accuracy but it will not accurately count steps if your arm is not moving.
The iPhone also counts steps and is used in conjunction with the watch if both are on you.
That's one of the metrics it uses (arm swing), but it can get data from other sources too. Accelerometer, GPS etc. I know it's worked for me when using a shopping cart. I didn't check for actual accuracy, but it did record steps. Would it be 100% accurate? Of course not. But in my experience, when I've specifically checked, it has recorded steps while using the cart, with my wrist that has my watch on the cart, not swinging by my side. I'm right handed and wear my watch on my right arm, so I'd actually expect to get poorer results than most.
I should check again though and see if those were steps recorded by the iPhone and not the Watch. I'm 95% sure it was the Watch, but not 100%. But again, it does use metrics other than arm swing.