Is there an animation for walking where a walking stick is used?

Not as far as I know. A possible solution is to have your character wield it as a weapon.

An example of what I'm looking for: http://www.youtube.com/watch?v=qy5_nBgwyn4 except for morrowind. Just the walk anim

New animations for walking sticks, no, I don't think any have been made.

The closest you'll get is http://planetelderscrolls.gamespy.com/View.php?view=Mods.Detail&id=7000.
Hold It also uses staffs in a similar fashion.

Hold it isn't available for the toon is it?

The staff meshes are set-up as shields, so yes you can equip them.