Is there a natural (non-product) of getting rid a smelly feet?

See below. Soak your feet in week tea. The tannic acid will help with odor & sweating.
Foot odor. You can try soaking your feet in a tea solution (wait for it to cool first). The tannic acid in tea helps dry and absorb odor. More importantly, see a podiatrist to find out the reason why there is an odor. It may be natural for you, but it may also be a fungal or bacterial infection.