Accurate step tracking with Apple Watch, without arm swinging??

I do not seem to have a problem when I am walking my dog and having the in my watch hand extended holding the lease.

I also have found out that with a pedometer on attached to your waist can be very inaccurate.

If you are outside and the watch is connected to GPS satellites it will estimate your steps based upon your distance and your normal stride. This will not work when you are on the treadmill as you don't actually cover any distance. I'm 71 and I don't hold onto the rails but I actually don't pay any attention to steps on my watch at all. Even though fieryjack's boilerplate didn't address your actual question he actually gave you a hint as to how to use your watch, on your treadmill pay attention to Move and Exercise rings and ignore how many steps you are taking. Apple deprecates the counting of steps as it isn't really a medical measurement. 10K steps per day actually came from a Japanese pedometer company that was mounting a sales campaign.

If you've got location services turned on then your distance/steps is measured with GPS as long as you meet this criteria;