I dont know which wallet lowest transaction fee but i use coinbase.its good for btc wallet
I don't think that the transaction fee can be manually set in Coinbase. If you want to manually set the transaction fee, then please use a desktop wallet, or an online wallet which allows that such as Blockchain.info. But first, you need to check the fee requirement, in sites such as bitcoinfees.21.co or estimatefee.com.