Answer: It sounds like you've inherited a lovely garden retreat! Salt would probably make the soil inhospitable to plants and soil organisms in your walkway, but there may be danger of the salt leaching into the soil and affecting the plants you want to preserve.
How about these alternatives? Some folks like to plant low-growing herbs, such as creeping thyme or dwarf peppermint, between flagstones in a walkway. The herbs grow into a mat, discouraging other plant growth, and as you walk, you're surrounded by the fragrance of the herbs. You could rent or buy a flame weeder, and burn off the weedy growth. You could also clean out the vegetation that is there by using a low-impact, soap-based contact herbicide. The active ingredients are fatty acid salts which kill plant cells on contact, but which do not persist in the environment. Once you weed the area, you could put down a thick layer of bark mulch, sand or other material between the stones to discourage growth in the long term.
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