Carrying a sword as a symbol of fire would make sense as a literary depiction. GEVURAH - power- sword - fire makes sense to me, but I am sure that the ceremonial dagger/sword serves as a symbol of air in the hermetic rituals.
For example, in the Lesser Banishing Ritual of the Pentagram from the Aurora Aurea when the archangel Raphael is invoked, he manifests himself as the representation of the Air element and is carrying a sword. Michael, however represents the fire element and is holding a wand.
Interestingly enough, Michael is often represented with a sword.
Obviously, the ritual magick symbolism is different from the literary symbols. The objects are the conduits of energy charged with the power of an element.
I wonder though, why Franz Bardon associates the objects/elements differently from what is common in the hermetic rituals.
Michael tramples Satan (Guido Reni, 1636)