How do I drop the item I selected when the wolf dies?

Sounds like you want to make a new Loot Table for the Wolf entity.  The Wolf's vanilla loot table entry is empty, so nothing gets dropped when killed.  This makes it no problem to replace it with your own.

Make a new Loot Table, lets call it "WolfLoot".

The Loot table registry name will default to "blocks/wolf_loot".  Change this to "entities/wolf".

Change the default Loot table namespace from "mod" to "minecraft".

Change the default Loot table type from "Block" to "Entity".

Add your desired item to the loot table pool below.