Crossing borders is a big advantage at the moment with Bitcoin, though it will apparently become the norm that the NSA will check your phone/computer to check for dodgy activity, including seeing that you don't have lots of Crypto.
There is no way to detect if you are bitcoin owner, or if you are transferring bitcoin within your smartphone, PC laptop, whatever device you have.
We can encrypt private keys and hid it somewhere, remember or write down mnemonic HD wallet seed or use dozen other methods to conceal your bitcoin stash.
If you are serious crypto holder then there is no need to worry about airport security at all.
I agree, you can just send the private key to your just created email address and access it after landing on your destination. It is as simple as that. You do not need to hide it somewhere. Besides this new email will surely does not link y our personal data because if you are a serious crypto person, you know how to make yourself anonymous.