Lack of citation means... well... we fall back on 18 USC 921.
Both the TSA and FAA's regulations deal with with "firearms" in this context (IE in carried baggage).
The meaning of the term, without additional clarification, can only mean default to the definition specified in 18 USC 921, which specifically excludes antique firearms from the definition of a firearm. There is, as you know, a second definition of an antique firearm. If I needed to argue it, I would state "if they intended to have the regulation be applicable to both firearms and antique firearms, they would have written 'firearms and antique firearms' that into the statute"
This is the "I'd rather be a wise-ass than a wise-man" argument.
A wise-man will treat them like a firearm, and if my experience is any meauser, it's a zero-loss to do so. I was encouraged by the ease of the process.