I would expect the same thing to happen. Your coins would probably split to both new chains.

But I would use either a hardware or offline wallet. For the hardware wallet, try companies like Trezor or the Ledger Nano S. Both corporations are setting up servers which would allow you to spend on more than one chain if there is a split.

For offline wallet, I’d suggest something like Electrum, or literally any wallet that does not have access to your private keys. As long as you have 100% access to your private keys, you should be fine. As the saying goes ‘if you don’t own your private keys then you don’t own the coins’.

One thing to abstain from doing is storing anything on an online wallet such as Coinbase or any exchange, like Poloniex. History has shown such a course of action to be an unfavourable one.