You can't force this change on other folk's computers. I control my PC and you may not make changes remotely.
But let's see if you can change/update this if it's your PC.
Try "View Profile" as noted at http://www.ehow.com/how_6945289_see-contact-picture-skype.html
I changed my profile picture on Skype on my iPad. Now how do I get it to change on other people's computers? My husband's Skype on his computer still shows my old picture.