I am not using Blockchain.com wallet, but there is still a recommended way you can have access to your private key. But this will require you to know the address you have the fund before the hard fork occured (you can track the addresses on blockchain explorer).
You will need to run
https://iancoleman.io/bip39/ offline.
Offline Usage
You can use this tool without having to be online.
In your browser, select file save-as, and save this page as a file.
Double-click that file to open it in a browser on any offline computer.
Alternatively, download the file from the latest GitHub release -
https://github.com/iancoleman/bip39/releases/latest/The address on blockchain.com wallet are legacy addresses (addresses that start from 1).
ProcedureAfter you have Iancoleman offline
Input your seed phrase from blockchain.com wallet
Note: If passphrase is added while generating the wallet (then it is required also)
Then, scroll down, you will see Derivation path, it is BIP44 by default
Scroll until you see the legacy addresses generated.
Then, scroll front to see the addresses, public keys and the corresponding private keys.
You can then get the private key you want. Likely the private key will be the first address. But, you can confirm any of the address to know if it has forked coins on blockchain explorer. But, it is more likely not beyond one of the first 20 addresses.