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.
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.
This is too much work and to get a shop to open up the phone and get all those removed it will not only cost a lot and chances of it working again is quite slim as the kernel is built around controlling this connectivity modules. What if they have an expensive iphone and or another expensive device?
It will be much more easier for them to just get a HTC Exodus 1S which has a secured partition specially for crypto wallet. Having one integrated with the phone is far more secured than running a third party app.
All in all, keeping a paper wallet in a bank storage would be so much easier and cost effective in terms or legally making a will in case something happens to the owner , etc or a trezor.
Just my 2 cents.