dodderer

/ˈdɑdərər/
noun
  1. A person who moves or acts in a weak, unsteady, or shaky way, often due to old age or frailty.
    • Despite being a dodderer, he still had a sharp mind and a good sense of humor.
    • The old dodderer shuffled slowly across the street with a cane.
    • The young nurse gently helped the dodderer into his chair.