There's no technological solutions to things like this, only political ones.
As a traveller, just before going through security you wipe your device and "sell" it to a vendor in exchange for a voucher that will allow you to exchange it back when you land and go through the security at your destination. You take the new device, provision it with your cloud data, and go on your visit; when you go back, you go through this process again, in the other direction.
Lots of problems to be solved with that idea, not the least of which is the business model, but it would allow you to travel without any electronics on your person.
You really want something that looks like an in-use device and gives no hint that you have sensitive files stored anywhere else.
Alternatively keep the main OS on a USB or hard drive, and get that in/out of the country by other means.
There are other options. Generally, carrying obviously visible sensitive files with you in person is not a necessity.
e.g. I send a partial key to my cousin and grandmother which live in another country. When crossing borders I then logout and cannot log back in without their part of the key. A local judge will not be able to compel someone in another country to cooperate - and my grandmother's local judge will not be able to compel her since the request is being made in another country.
Kind of hokey - but maybe it works?
If you do not have even the ability to comply, justifying contempt becomes increasingly difficult.
Here's another example that might make this more clear. Let's say I embezzle a million dollars from my employer, and they sue me to get it back. (Let's just pretend that I avoid criminal charges for simplicity.) When they win and I tell them, "I can't comply, I gave it to my cousin in France to hold on to," what do you think the judge does? I'll tell you what the judge does: https://en.wikipedia.org/wiki/H._Beatty_Chadwick (This only applies to the U.S.. I suppose in the U.K. you would do two years and then be released.)
The problem is that HN-types want to assert cryptographic power over agents of governments, ie I won't show you my files and you can't make me so I win.