First of all, there is no "private key at the time". Your wallet does not have one private key which it changes for each transaction or on a time basis. Rather your wallet contains multiple private keys, one for each address you use. It is not one private key per transaction.
Secondly, the ID in the exported .csv file is not the private key. In fact, there is no way for your wallet's private keys to be exported from the GUI. You will need to open the debug console (Help > Debug Window > Console) and use the dumpwallet or dumpprivkey commands to get the private keys. The private keys will always begin with a 5, K, or L. If they do not, then those are not valid private keys.
However you should not need to export your private keys to import into a Bitcoin Cash wallet. You can use a Bitcoin Cash wallet which is based on Bitcoin Core; such wallets read and use the Bitcoin Core wallet.dat file.
So to be able to spend your Bitcoin Cash, first move your Bitcoin to a new wallet. Then download and install a Bitcoin Core based Bitcoin Cash wallet such as Bitcoin ABC, Bitcoin Unlimited Cash, and Bitcoin Classic Cash. Then copy your Bitcoin Core datadir (which includes the blockchain, the databases, and your wallet.dat file) and have your Bitcoin Cash client use it. You may need to have it reindex the blockchain. Once that is done, you should be able to spend your Bitcoin Cash and use the Bitcoin Cash wallet software as you normally do with Bitcoin Core.
