You don't have to transfer bitcoin. You can give someone private keys to the wallet and they can do anything they want with it. It would be exact equivalent of giving someone the bill
You do have to transact bitcoin to get bitcoin into the wallet. Plus, you can't prove to someone you haven't kept a copy of the private key, so you can't really transfer ownership of a private key, not trustlessly.
You do have to transact bitcoin to get bitcoin into the wallet. Plus, you can't prove to someone you haven't kept a copy of the private key, so you can't really transfer ownership of a private key, not trustlessly.