You can't claim BCH without knowing private key, even if you withdraw that Bitcoin to your BTC wallet. Because, it means that you will get Bitcoin into your wallet after BCH fork.
To claim BCH, you have to have Bitcoin on your wallet before BCH fork.
If you make a BTC transaction, it is not possible to broadcast the same transaction in BCH network manually. BCH uses "sighash_forkid" to distinguish, so BCH won't accept the transaction that you made and broadcasted to BTC network.