You are having the feeling on wrong way because it is totally an opposite thing where you do keep your tokens on an exchange. Havent you seen the recent or past situations of exchange hacks? If you are then you can able to identify yourself about your current situation if its still safe to put up or store coins in there. Even just using your own wallet and do only have your own access you can still have the risk on getting hacked depending on how safe you do keep up your keys.