So it's mentioned that the Ke-Han have fireworks. Meaning they're perfectly capable of making something that will fly high up into the air and then explode. Why do they still bother with the catapults?
Since the dragons are made with magic, it's not unlikely to assume they have fire-warding spells or something on them. Fireworks would kill the airman, but the dragon would just return another day with another rider. If they got hit with a large boulder, though, repairs would be expensive, maybe even impossible, or if the Ke-Han are really lucky, the dragon would be knocked out of the sky somewhere they could collect it to study it. There's also the matter that fireworks are more unpredictable than catapults, and it would take a lot of firepower to get enough gunpowder in the air to take out a dragon - one misfire and they're doing the dragons' work for them.