I walk sometimes reading Twitter or ebooks on the iPhone 6+ and it accurately measures my steps even though I am holding it relatively steady. I have compared steps recorded on known trips with reading and with the phone in my jeans pocket and they match well.
So I think the watch will do just as well, if not better as it has the M7 in the iPhone as a second source.
So give it a go. Try one street and then repeat with the other hand and see what happens.