The OP mentioned a roughly "age of sail" level of technology with some alternate history in there to permit early development of lighter-than-air flight. This is a kind of Steampunk.

**Chemical and biological weapons**

People have known about noxious substances for a very long time. Perhaps they did not know of their true manner of operation, but they knew that catapulting dead animal carcasses into an enemy fort could cause an outbreak of disease.

Airships could be loaded with chemical and biological substances - maybe vats of acid that could be poured out onto ships below (leading to dogfights in which "getting on top" is key), or water balloons filled with whatever poison floats your boat (or sinks your enemy's). Ships holds' could be filled with trash and decaying waste products to be used as ammo in catapults and slingshots. There's nothing like another trip to the dump to reload. Even the rotting carcasses of enemy soldiers could be used.

**Gliders**

Ships could be equipped with basic gliders that could be launched in order to land boarding parties on other ships. This would be another case where "getting on top" would help, since the gliders would be unpowered. Once a boarding party has landed, they could use more conventional age of sail weapons like swords and firearms.