FaucetHub takes a 1.5% fee off of any coin deposit right off the bat, so there is no getting around that.
People are sending transactions with one satoshi per-byte fees, so that can't get any lower, really. 1 sat/byte fees confirm within 30 minutes - 12 hours.
sourceHowever, there are exchanges that cover withdrawal fees. Gemini will cover up to ten withdrawals a month for free.
sourceGdax also covers withdrawal fees, but they are a part of Coinbase. They can also take a few hours to send the tx out to the network as well.
Either choice isn't a bad one: either you pay 1 sat per-byte or you don't pay any at all at the expense of an exchange having a record of your identification.