Get real.
“Nice try, but nonsense.”
The only nonsense is your nonsense denial of the documented fact in the dictionaries that define these words. Look in a Merriam-Webster dictionary, which serves as the standard reference for American English. You can find the word “fire” is defined as an intransitive verb meaning to “to emit or let fly an object.” You can also find the definition of “arm” as another intransitive verb meaning “to furnish or equip with weapons.” The words, “fire” and “arm” compounded into one word then means “to emit or let fly an object...to furnish or equip with weapons.” You will note there is nothing in the definitions requiring the weapon to emit or let fly an object by the means of combustion. The Balaeric sling used in the ancient battles was certainly purposefully designed as a weapon to let fly an object without the means of the combustion of gunpowder.
“Is a simple catapult a firearm?”
Yes, because it was purposefully designed to “let fly an object” as a weapon.
“Is a blow gun a firearm?”
Yes, because it was purposefully designed to “let fly an object” as a weapon.
“Is a mouth spitting a gob of phlegm a firearm?”
No, because it was not purposefully designed to “let fly an object” as a weapon.
If you want to dispute the written definitions, take it up with all of the publishers of the American English and English dictionaries such as Merriam-Webster, and don’t falsely accuse the judge when he uses the common dictionary meanings of the words.