I agree with the first two. Those are distinct weapons in Fire Emblem but are Aymr and Armads are mythological weapons. Some other FE weapons have qualifiers, like yato_(fire_emblem). I don't think Mani Katti needs it, as it is not a mythological weapon and instead random mashing of fun sounds words from two different languages. Levin sword doesn't have a qualifier and that's ok, it's very distinct.
However, none of them implicate the underlying weapons themselves, nor should they. Armads, for example, is actually a sword in mythology and wasn't always an axe even in the game. There was that weird time it was a mattock of some sort. No other specific weapon tag implicates their base weapon.