Any exchange, even Yobit, can do what you want. Poloniex isn't bad, and they're one of the most reputable nowadays. The fees on both Yobit and Polo are pretty reasonable, just don't keep any coins with them. Then there are Chinese exchanges...but I'd stay far away from China if I were you. They're doing some major 'renovations' with respect to crypto and the law.
My understanding is that Shapeshift doesn't have "fees" - only mining fees. Is that the same with the exchanges you recommend?
They do. You get charged hidden exchange fees that you pay more than if you were to do it at any other exchange.
Do it cause of the instant exchange of alt to btc or alt to another alt coin. But the fee's are put in as "the rate" they charge you to do transfers instantly on their site.