A general word for weapons which are not considered firearms

Cold weapon (also known as white arm) seems to be an appropriate word.

It refers to weapons that do not use any sort of explosive force in their function. It comprises blunt (knuckles, maces), edged (swords, knives) and ranged (bows, crossbows) weaponry.

Here is the relevant excerpt from Wikipedia:

A cold weapon (or white arm) is a weapon that does not involve fire or explosions (such as the act of combustion) as a result from the use of gunpowder or other explosive materials. Ranged weapons that do not include gunpowder or explosive materials and melee weapons are cold weapons. Firearms and explosives (such as grenades, land mines, missiles, bombs, etc.), and other weapons which rely on heat or burning are not cold weapons.