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.
I think maybe it really depends on what wallet provider in your country but most if all Filipino using coins.ph and it has no fee in every transaction deducted to every transaction made by the user and also it is user friendly with different features like buying steam and even load and also we can do easy cash out.