When playing a game with Warheads and Light Artillery (https://mods.factorio.com/mod/lightArtillery), it has no warhead ammo types. I would've tried to add them myself with the documentation you provided in the Information page, but those links are dead. Perhaps they're pointing to the wrong version of Warheads? (0.0.1 instead of 0.0.11)
Note: Since the light artillery ammo is intended for early game, perhaps only thermobaric warheads could be attached. You could also argue that all the warheads are too heavy for the light artillery to fire and everything is as intended (no options to add warheads to light artillery ammo).