Can I make entities hit by a custom snowball run a custom command?

I want to detect custom mobs getting hit by a snowball with custom NBT data, it looks I can do that in predicates? How would I go about it? I'm redoing Ninja Stars basically to be just snowballs that deal higher damage. 
This is for 1.20.4 I assume the code would go something like ```{
  "condition": "minecraft:damage_source_properties",
  "predicate": {
    "source_entity": {}
  }
}
Would this work