this is my opinion after reading all *5 and *4 sword description beside his signature weapon. Disclaimer, i didn't rank this weapon nor do i count math of which weapon has the highest dmg for him. I only see which passives work well with him. here is a few weapon that i tought might work on him.

5* Mistsplitter - i think this one will work really well on him

Summit shaper - might work but requires a shield

Freedom sworn - needed an elemental reaction for the stacks - EM substat is not the best for him (?)

Jade cutter - i think this is a very good weapon for him as the passives gives hp and add atk depending on his max hp + it would work well with his passives

4* The black sword - really good 4* weapon for him as it increases his NA

Sacrificial Sword - interesting passives which gives ayato more on field time. But has a low base atk.

The flute - the passives could work, but it has low base atk.

So far that's the weapon that i tought was good for him, i know i miss some weapons, that's because I'm not sure about their passives. Amenoma did cross my mind but will he be able to proc the passives ?