There is no reason to think he doesn’t need his wand for actual Dementor crushing. The Dementor scaring wasn’t him casting anything. It was due to Dementor’s own ability to commune with Harry turned against it (plus, hypothetically, some expectation manipulation—the “BOO” there was probably more than just for show, but also to prime Harry’s mind into expecting the thing to be spooked).
Normal wizards need their wands and the ability to cast patronus in order to deal with a dementor on their own.
Harry can deal with dementors without his wand. That is, they cannot eat away at him. He can stand in their presence without becoming demented. And that is unusual.
There is no reason to think he doesn’t need his wand for actual Dementor crushing. The Dementor scaring wasn’t him casting anything. It was due to Dementor’s own ability to commune with Harry turned against it (plus, hypothetically, some expectation manipulation—the “BOO” there was probably more than just for show, but also to prime Harry’s mind into expecting the thing to be spooked).
Normal wizards need their wands and the ability to cast patronus in order to deal with a dementor on their own.
Harry can deal with dementors without his wand. That is, they cannot eat away at him. He can stand in their presence without becoming demented. And that is unusual.