if you need just to trade coins to coins then I'd rather use pair of wallet + exchange. I use Jaxx.io and coinmonkey.io platforms.
Jaxx wallet seems to be quite safe because you safe data on your own side including private key, backup phrase and you can not access your wallet through any website. only using application.
Coinmonkey.io is platform which scans exchanges for rates, so you can choose exchange rate at their website and actually perform the transaction via their api widget from exchanges (as far as I know they are partenrring with exchanges), so one can exchange directly from the wallet.