Coinbase is not secure at all. Do you understand why private keys exist?  Private keys give you the right to your funds, by using coinbase all you are doing is simply putting your money like in the bank and thus you trust them. First of all they can get hacked and lose funds, secondly they can freeze your account and lock your money away from you.

What blockchain wallet are you talking about? There are many lightweight wallets out there and you will have to be more specific as it is hard to guess and tell you something. Mostly they have to have like faq or something where they explain this.

You can use tool such as coinb.in to craft transaction offline by yourself.