Paper wallets are old school but quite secure;
https://en.bitcoin.it/wiki/Paper_wallet
No, your Bitcoin does not have to be in an exchange. It's all about the private key so, if anything, a paper wallet is better in a forking situation than an exchange. Ahead of the BCH for, Coinbase warned people to take their BTC off the exchange since they were not going to support BCH. I did so but forgot to do so with a small account I had at blockchain.info
Never did see any BCH turn up in my account there.
oh wow sorry to hear that :( thanks for sharing and explaining!