There is no apps, exchange or other think can reduce your gas cost ~XD
The gas always depends on the current network and the "Gwei + Gass Limit" you are using for the transaction. I believe the wallet you are referring is the wallet you can control by your own, you can use Metamask/Trust Wallet.
yes, that's right no dex wallet can reduce the gas cost as it depends on the network congestion. metamask, MEW, trust wallet are known dex wallets. as long as you know how to secure the keys of this wallet, you have the full control on what's going on with your portfolio.
and in terms of exchange, just check the fees involve but dex with good liquidity will be uniswap, pancakeswap. you can also check the cmc for this -
https://coinmarketcap.com/rankings/exchanges/dex/