I don't know much about Quail, but I'm a bit confused.
This is a 3week old chick, he's able to walk, eat/drink on his own and preen?
Doesn't sound like there's too much wrong if he's able to do all that.
A video of actions may be helpful - upload video to youtube and provide a link.
Walking in circles from trauma - I would give him vitamin therapy. Do you have any Poultry Nutri-drench? If so, give him .25ml once a day. Otherwise, give him 400IU Vitamin E and 1/4 tablet B-Complex.
As for culling a tiny chick, using shears or scissors is the best method. Read this article
https://www.backyardchickens.com/ar...-for-squeamish-people-slightly-graphic.74734/