I haven't tried copay, but I've used Mycelium to read a QR-code from a paper wallet, then read another QR-code from the site I want to send it to. This way, the phone wallet is only used to create the transaction, and never used to store funds.
Note that you have to send the entire balance at once. In Mycelium, I click "Max", and it only takes out the transaction fee. If you were to use a part of the paper wallet, the change is send to a change address, and not back to your paper wallet.