I believe you can accomplish your goal by installing Qubes OS with detached headers in a USB drive. You can then cross the border without the USB drive.
(Unfortunately, I tried the steps in the post and they didn’t work for me; maybe they’re outdated. If you get it to work, please write a post.)
My understanding is that, without the LUKS headers, the data in the laptop looks like random garbage. If asked you can say the laptop can’t be booted (true).
After crossing the border you can get a copy of the LUKS headers from a friend, Nextcloud, OnionShare, snail mail, etc.