You don't have a
wallet on LocalBitcoins (or Coinbase, or any exchange for that matter). You have an
account. People call it a
wallet, but it is not a
wallet. It is really just an
account.
If you want to withdraw BTC from your
account, you have to send it to a
wallet that you own (or perhaps send it to another
account).
I see, but that way I don't own the original wallet, and have to pay fee for the transaction.
As explained above, you already don't own the address (or the wallet). The fee for sending BTC is generally about 5 cents. That doesn't seem like a lot to me. You could pay the fee and be done with it.