Uniswap is a DEX which means no one is storing there token in there and not related if your main subject is not your keys, not your coins against using a centralized exchange.
This is a very important clarification of the term as I observed that, any member are miss representing both means one, DEX exchange, gives you the right to hold your coins in your private wallet, and any time you want to swap you will need a wallet connection to the Dapp site to initiate the conversion.
On the other hand, centralized exchange hold your assets and does not give you a wallet key to recover your asset. any point, so the holder becomes not in control of the wallet.