We consistently have "no salt added" tomato products in northwestern Ohio
which I use regularly--Del Monte, Campbell's, and Contadina. Tomatoes
naturally contain some sodium so read the ingredients label. The larger
groceries carry "no salt added" tomato paste, juice, puree, etc.
Beans are a problem and it took me quite a while to learn to cook dried
beans. For one thing, soak them over night; but always rinse and change
the water before cooking them the next day. During cooking, never add cold
water. If you must add liquid, warm it first.
We also have other "no salt added" vegetables such as green beans, peas,
carrots, etc. Just read the labels every time you buy. One doctor
suggested draining the brine off the canned vegetables and rinsing with tap
water; then heat them in the microwave oven.