Is exchanger wallets safe?
people already explained to you about risks of using online web wallets as your storage especially in exchanges which can go down.
but from what i read, it seems like you are not using your bitcoins for long periods of time, in that case you should use a cold storage like paper wallet instead. you keep it in a safe place and only receive payments in.
Paper wallets too cannot be secure as when people tend to forget their password and lose their private keys, they can lose those wallets too. Physical wallets can be the best option but only if you have a good amount of bitcoins to store.