You don't need an exchange for this. If you have the private key, you have both Forkcoins already.
You can use an exchange though if you want real Bitcoin instead of Forkcoins Just read my post above, the lack of replay protection is important, so don't instantly send your coins to an exchange: if the coins move on both addresses, one of them won't be recovered by the exchange. Split them into separate wallets (for which you control the private key) first. That way, if they end up on the wrong chain, at least you can access the private key to fix it.