Moving with a weapon in your hand. (a bokken) Purpose is what matters and only a demo or dedicated class to such a weapon would fit your description. I could use it as a walking stick to demonstrate a point if I want to.
I've actually seen Saotome Sensei use a bokken as a walking stick. And many jo forms start from a hiking staff grip.
No matter what the purpose, the way a person holds their own body, with or without a weapon, is extremely revealing.