Ignore me if I sound stupid but how would you download the app when your phone is on the airplane mode? It needs the internet to download the App right? 
Pretty sure you need to be online first and then switch to airplane mode, or download from another phone and send it to your 'wallet phone'. In both cases, it still needs to connect with the internet or another device, and not as 'cold' as you think it would be.
Once you download our app on an Android device, you must keep this device in airplane mode as long as the app is installed.
You can also (as I did myself) ask your local mobile shop to physically remove remote connectivity from your device (i.e. remove sim card slots, wifi modem, bluetooth...) before using our app.
In any case, once offline (in airplane mode or after physically removing all connectivity), you can use our app to create your wallet with your own entropy and offline-sign transactions via exchanging QR codes.
This way, by design, your secret keys are really yours (created with your own entropy) and are always kept offline. This is the definition of a cold wallet as you can see here: https://en.bitcoin.it/wiki/Cold_storage