There is case law in the US to the effect that knives are covered by the Second Amendment.
Here, linking the right to own and carry knives will be a 2nd Amendment issue, as States will start to restrict the possession and carrying of knives as England is doing. It will just take some dramatic murders committed with knives to create the emotional fervor among certain people to ban them. "They're inexpensive, unregulated, silent and lethal, we must get rid off them!" will be the cry. It's utter rubbish, but it's coming.