Ah, should have probably specified that the cadillac horns are also electric.
I've heard of people replacing the stock horns with electric ones from Wolo or Hella. While they're loud, the tones are shrill and unpleasant to me. I wanted something with a bit of a melody to it. That's why I originally wanted the trucker air horns.
Anyway, I found this momentary pull switch which would be able to replicate the feel I want to go for if I were to mount them on their own relay. It's like a reverse push-button solenoid. You pull on the stud to close the circuit, but a spring pulls it back open when you release it. I just need to figure out what the best way to wire these horns is so I can leave the stock one alone. I know it would be easier to just replace the stock one, and I'll probably end up doing that if the idea I have ends up being too complex, but I would like to try leaving them separate if possible.