Aren't there some disadvantages in arguing for knife rights via the Second Amendment?
1. We want tools, not just knives. We still won't be able to carry a pry bar in some places. I'd rather be able to carry a pry bar and a fixed Mora knife than a switch blade, an auto, or a "combat knife."
2. This strategy may deepen the impression of the general public that knife = weapon. That will result in a push back. Also, if we argument that the Second Amendment extends to knives, then it also extends to swords, halberds, spears, etc. It's hard to see how the American public will accept that. America is a gun culture, not a medieval weaponry culture. People will accept conceal-carried guns before they accept a morningstar.
3. Finally, we don't want the same sort of gun restrictions to be applied to knives: no knives near schools or federal buildings. Employers might be motivated to create "knife free zones." Stores might be pressured to start a "no knives" policy when they just want to make a buck.