The closest parallel is probably an EMP strike. They're designed to inflict 0 casualties, but they cripple the enemy. That mirrors the usage of offensive software; they don't inflict any casualties directly, but they can ruin supply chains, remove communication capabilities from the enemy, etc.
They probably deserve to be classified as weapons, and banned by a subsequent law. I think the government has a compelling case that would almost certainly pass strict scrutiny. It seems a logical place to put them, because they are dangerous, and the strict scrutiny puts an onus on the government to use the least restrictive means possible to legislate them. I fear the alternative is that they aren't classed as weapons, and we get some overly broad CFAA type legislature that threatens to penalize security researchers.
SCOTUS says that the 2nd applies to weapons which are “bearable”, i.e:
> "“[w]eapo[n] of offence” or “thing that a man wears for his defence, or takes into his hands,” that is “carr[ied] . . . for the purpose of offensive or defensive action.”
Pretty hard sell that it's a "military" weapon when you can carry it around on a thumb drive.