IME: Much work was slower while walking:
Reading: My head was moving relative to the text; reading was much slower.
Typing: My arms and thus hands were moving relative to the keyboard. Perhaps typing on a phone screen would be better, as it can move with you.
Using a mouse: Tough to do while walking.
Talking: Obviously people walk while talking on the phone, but notice that they stop when they have to concentrate. As another example, talking on the phone while driving sometimes results in a failure to do one or both.
Thinking: Walking can be good for getting the creative juices flowing, but I find it hard to walk and really concentrate hard on intellectual things.
But having said all that, I would give it a try: What you do, how you work and walk might be different. Maybe you'll find better solutions. Worst case is, it doesn't work out.
