Would they have been as upset if she’d been carrying a hatchet or a machete?
You make an excellent case. Edged weapons such as knives, swords, and tomahawks are clearly protected by the second amendment. Perhaps moreso, because swords were specifically mentioned during the debates about ratification.
Have to find the right test case, though.
Most schools have a restriction on blade size, if they allow edged weapons at all. And some states have restrictions on lade size for concealed edged weapons...to the point that a good sized pocket knife could get you in trouble.
And, many states have a vast array of laws governing locking blades, fast open blades, etc. Its hard to keep up with.