There are a couple of wallets that let you choose custom transaction fees. One of them is the electrum wallet, I use it myself, by far the best free non-hardware wallet. It's extremely lightweight and works like a charm. I highly recommend getting that if you want basic user experience and full control for free.
As far as I know, recently, there are not any wallets that are free of transaction fees for us. The value of bitcoin increased, the number of users also increased significantly, they must use transaction fees to maintain the speed of each transaction.