I think you're confusing wallets with exchanges.
A wallet gives you and only you full access to your private keys and thus funds, and (depending on the wallet) lets you set the fee.
An exchange doesn't give you access to private keys, and you'll have to jump through whatever hoops they come up with.
In short, download and install
Electrum (make sure you use the real site, there are many fake sites trying to steal your funds), and set custom fees.
However, know that low fees could mean it takes a long time to confirm your transaction, and collecting small amounts of Bitcoin can lead to higher fees when you want to spend it. See
Fees are low, use this opportunity to Consolidate your small inputs!