The only solutions to manage BCH on your Ledger device if the BTC were not on your Ledger device at the moment of the fork are:
- to send some BCH to your Ledger wallet from your current wallet.
See How to transfer Bitcoin Cash to my Ledger? Where can I find my BCH address?
- to import a compatible 12, 18 or 24 words seed on your Ledger device by following this: Backup: 24 words seed and compatible seeds
Sending only BTC won't be enough, as the BCH could remain in the first wallet.