For your consideration, here is a Clothes Dryer Timer Dial Knob, no. 299371, 1-N, used.  It has a little wear on it.  It has a diameter of 3 5/8 inches.  It will be mailed in a box for protection.  Item pictured is the actual item up for sale and comes from a non-smoking household.  (436.756k-.7bx3)