Okay, look, I think people get way too hung up on 'origins' for things like Nanami's blunt cleaver. It's not some ancient artifact with a grand backstory. Gege Akutami just needed a weapon that mirrored his personality and fighting style. He's a salaryman-turned-sorcerer, right? Pragmatic, no-nonsense, highly efficient. A regular sword would be too flashy. So he gets this industrial-looking cleaver wrapped in cloth, like a tool. The cursed technique isn't in the weapon; it's his own Ratio Technique. The 'tool' is just a focus for his precise, devastating strikes. The lore is just 'it's a cursed tool he uses'. Sometimes a weapon is just a weapon because it fits the character's vibe perfectly, not because it needs a lineage.
Honestly, I prefer it that way. Not every cool thing needs an elaborate flashback. Its origin is basically 'bought from or made by a jujutsu society craftsman'. The real story is how he uses it to embody that theme of measured, professional violence versus the chaotic curses.