On the forums it seems like it is possible to walk with your character using a controller, but I can't find a keyboard shortcut that does the same thing. Am I missing something?
One of the biggest difference between a keyboard and a controller is that the directional input of a keyboard is digital (discrete set of values; in this case, binary -- pressed or not pressed), while the input from a controller's thumbstick is analog (continuous range of values)
The short of all this is that if you're using a keyboard, there's simply no way to move at less than full speed -- there's just no button implemented to move forward at half speed (or whatever).
The closest you'll get on a PC is entering stealth mode, which will slow you down and make you crouch, but this isn't actually a "walk" mode, it's just slower.