I'm not sure why no one mentioned this. But if you're in the US (and maybe other parts of the world), the 0 fee exchange with the cheapest way to replace coins is gdax.

It requires depositing fiat via coinbase, then transferring that fiat into gdax, then use the limit orders to buy your desired alt for 0 fees. After buying your coin you can send your crypto anywhere for free because gdax doesn't charge a withdrawal fee. Literally free of fees.