I know that customizing the network fee is possible. I was mainly thinking of flat-fee wallets from exchanges.
I need to have the ability of knowing the transaction fees beforehand.
I don't think if there's wallet like that, as a customizable transaction fee, like blockchain.info(suggested above), electrum has that feature also, and mycelium but you can't manually edit it but there's a 1 sat/byte fee option there.
And as what others said and what I posted all over and over, that the same wallet provider like coins.ph and coinbase doesn't require a tx fee in every transaction. And with exchanges that requires a minimum fee, like Bittrex with 0.001 BTC and the same with other exchanges.
And knowing the transaction fee, first you have to know what is the size of your transaction before sending, and in mycelium wallet, you can see the size if you want to send BTC so that you can easily know what fee is suitable for the transaction.