It seems some members didn’t get OP’s point. What he is looking for is a solution that allows him to send crypto even if he doesn’t have enough of the native coin to cover the fees. Like being able to send USDT (ERC-20) without having enough ETH to cover the gas.

Unfortunately, I'm not aware of any wallet that can do this (be it a web wallet or not). This isn't possible even in wallets that have an internal swap feature.
The only thing I can think of is using a centralized exchange like Binance (no need to remind you of the risks involved as you seem already aware of that). Withdrawal fees aren’t that high, except for Bitcoin and Ethereum.