Start in a Handstand position; you should already be comfortable holding at least 10 seconds at a time in the static position before attempting the walk.
Shift your weight to one hand, taking care to keep the Shoulder elevation on that side.
At the same time, shift your weight slightly forward.
Quickly move the free hand forward to catch you from falling.
Keep alternating sides; congratulations, you are walking!
It will take a while for you to get used to the motion but don't give up, the walk is within your reach.
Risks
Always warm-up your wrists thoroughly before working on such exercises.