..So if you do not use any of the two currencies (BTC and BCH), would I be safe?My plan is to keep both coins and see what happens

Post-HF transactions on the BCH chain use a different sighash algorithm (it's adapted from BIP143) to compute the transaction hash that the spender of the output signs. In other words, the transaction hash of a post-fork BCH transaction prevout is completely different data than the transaction hash of its corresponding prevout on the BTC chain. The signature is signing different data on each chain, so each chain's signature is invalid on the other, making transaction replay impossible.