Commercially Weleda, Tom's of Maine, and HomeoDENT carry mint-free toothpaste.

The best whitening toothpaste I know is black walnut tincture mixed with powdered white oak bark. Well, it's not so much a paste as a mildly gritty slurry. ;-) Removing both plaque and tartar it gently whitens without bleaching. It also helps receding gums and is reputed to re-enamelize soft spots and cavities.

IMO the traditional toothpaste baking soda/salt paste is a much less effective whitener. I really don't like the taste so, for busy mornings, I keep a little jar of baking soda whizzed in my blender with dried sage. You could blend the baking soda with any other herb you enjoy.

HTH,
Cheryl