Make snowball damage

How do i make a snowball do damage
I had a way to make it do damage but it also hurt the player that threw it, so as a a solution I made it ag the player but that didn't work cause now it tags every player it goes near, please help

execute as @e[type=snowball,nbt={Item:{components:{"minecraft:custom_model_data":{strings:["boaterhatprojt"]}}}}] at @s if block ~ ~ ~ air run damage @e[limit=1,type=!marker,type=!item,type=!experience_orb,type=!armor_stand,type=!block_display,type=!item_display,type=!interaction,distance=..1.8,tag=!thrower] 5```

 I need either a better tagging system, but preferably a new damage system