Blockchain transaction fees don’t apply when you’re trading on an exchange. They only apply when you send your bitcoin to the exchange from your wallet. When you have your bitcoin in an exchange and not in a wallet, then it’s in the exchange’s pool of bitcoin and they do their own internal accounting for what belongs to whom - changes aren’t made to the blockchain ledger for every trade on exchanges. This is why people say to not store your bitcoin in an exchange long term, because exchanges are prime targets for hackers with these large pools of cryptocurrencies, and you’d lose your funds. There’s no insurance on these accounts.
I think shapeshift exchanges are on the blockchain, which means that the blockchain transaction fees would apply, and so it would be more expensive than exchanges right now.
Exchanges may charge a commission of like 0.1% or something like that for each trade.
I store the vast majority of my cryptocurrencies on hardware wallets. I only have 2 altcoins on desktop wallets that I keep on a cheap laptop that I don’t really use, so it’s off most of the time and pretty secure.
I haven’t bothered getting wallets for a few alt coins that I own, and just store them on the exchange, but I also own very little of these. If I have more than a couple hundred dollars in something then I’ll get a wallet for it.