I too was great fan of wallets like Electrum until I lost my coins due to some hacking and worst part was I can see my coins going but I cant do anything to stop them. There is no way I can recover them. Exchanges like binance are safe in a sense that they provide features like 2 way authentication that keep your assets safe. Nonetheless, if you can take little bit care of your wallet (be it cold or any other) then go for it. Since you have the keys, you own the coins.