First, knives may not be "arms" within the meaning of that term as easily as guns for which arms may be an abbreviation of firearm. Second, the militia clause is usually seen as limited the scope of the amendment to the National Guard or its equivalent. Finally, and most importantly, most of our 1st amendment freedoms have been applied to the states and local governments through interpretation of the 1st and 14th amendment (due process). The Supreme Court had not done so with the 2nd amendment as of the late 1980s when I left law school. (Anyone out there more up on this stuff?) So, even if the 2nd amendment applies to knives and the militia clause does not limit the applicability of the amendment to the general public, you still have an up hill battle applying it to the states, counties and cities where you live. I don't like it. I think the blade length laws are silly. But,I doubt I would win an argument that they are unconstitutional which is what I think you are asking.
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