I never thought about toothpaste.

Drug dogs are trained to smell drugs, packaged in plastic, wrapped in tin foil, and hid in coffee or peanut butter. Point being, if you are the least bit concerned, hang it. Some animals sense of smell are incredible.
Better safe than sorry.

As for your pack, I would "think" keeping all of your food in a separate bag inside your back pack would keep it clean of scent.