I think the best way to keep your Bitcoin during fork is on hard wallet or paper wallet. But since I don't have any of this, I decided to use my Bitcoin to buy more alts during fork because that is the right time to buy more alts due to cheaper prices. I will wait till its prices rise again after the fork. I don't suggest that you keep your Bitcoin on exchange wallets. It is too risky for me. Better to put it in an offline wallet or downloadable wallets if you don't have hard wallets or paper wallets.
Such a much secure manner of holding is not required. On my view, it's good to keep hold in whatever the wallet might be with the private keys in hand. Importantly during the past fork too, mine were in the online wallets and periodically they used to give notifications that so an so not be done till the targeted time. Finally everything was safe as it was there before the fork, this time too all my holdings were on the same wallet.