You say that, but put in the situation you'll find your bravado is significantly lessened.
1) use FDE with a LUKS-like scheme where the encryption header can be backed up and then removed (making sure you can restore it at your destination somehow).
2) Destroy the header before travel. Carry live media if you need to use the machine while traveling but keep it minimally provisioned (nothing personal on there).
3) Your machine essentially now contains random data (even to you), perhaps except the partition table and/or boot parition(s). Tell the authorities that you "fill your hardisk up with random data before traveling in case of theft."
This is a true statement because: a) without the LUKS header your own data is essentially random, even to you and b) the scheme does protect your data in the event of theft.
Thus you can safely utter it with no bravado.
An even better scheme would use verified boot of some kind so that if the device is confiscated and returned, and its critical to you, you may have some way of proving the boot loader hasn't been tampered with. But I can't speak as to the difficulty of this.
Better yet, tell them your laptop broke while in the airport before boarding the plane, and you are going to buy a new harddisk/get it serviced when you arrive at your final destination. Much more plausible.
It's a felony to make false or deliberately misleading statements to U.S. border agents. Unless your laptop actually broke while in the airport, performing the scheme you described is a felony.
If you removed a key header which is crucial to the operation of your device in the airport, then the question is whether you can legally say, "my laptop broke in the airport," even if it was you who deliberately broke it.
This also covers the case of the question, "Does this device contain personal data?" To which you can truthfully answer, "Yes."
The point, in my original scenario also is not to lie, but to simply avoid being able to provide access under duress.
Why not whipe the disk and enter with a clean system if it's so critical?
wrt giving up the key under extended duress, I was thinking the same thing and aside from simply wiping the disk I can think of another scheme that might serve you well: give the header to a trusted 3rd party who could simply be the one actually controlling access to your data. Your lawyer for example.
Do you have personal data on this device?
and you answer No (when you really do), then you're looking at 5 years in prison under §1001(a)(2). https://en.wikipedia.org/wiki/Making_false_statements
A much better method I have heard is to ship your electronics beforehand, travel with only a burner cellphone, then pick up the electronics after you arrive. Repeat when traveling out of the country.
Sounds like a sure-fire way to get them to harass you more and pay closer attention to yourself.
I still believe there is a way to adjust such an encryption scheme to meet the ideal criteria:
1. you're not lying 2. you can't provide access 3. you're not drawing extra attention to yourself
If you have relevant data, then you simply don't cross borders with a device containing such data (or with a computer at all). This is just common sense. This "plausible deniable encryption at the border" nonsense is just a cryptonerds imagination.
And you just made yourself a suspicious person to be further questioned and searched, while probably committed an offense that could send you to jail.