I think that regardless of the fact that there are a lot of fancy methods that could work at customs, it might be best to temporarily store the seed in your memory, especially if we will do a wallet recovery relatively soon after leaving the airport. If someone has a problem remembering 12 words, maybe he could try to remember only 6 of them, and save the other half on a piece of paper that can look like a list of things to buy or something similar.
It's very individual. For those who have ADHD or are inattentive, it won't be a reliable solution but those who believe in their mental abilities, they can do it. Btw I have read many times on Bitcointalk that it's not recommended to make yourself dependent on your memory in this case.
What I would never do is carry a hardware wallet with you, or have wallets installed on your smartphone or computer, especially if you are traveling to countries like the US, Canada or Australia that have very aggressive security in their airports when it comes to customs, especially if you come from countries that are on their suspicious lists.
I think that OP will be safe if he travels with his computer. If I remember correctly, he wants to move in Europe. I've traveled in EU a couple of times but their customs were always great in my case. I can't imagine any custom asking you to open your PC, then force you to type password and then do a deep scan of your computer files. As far as I know, their priority are guns and drugs, besides that they don't care
A friend of mine has migraines and when I visit him in Europe, he asks me to bring one particular NSAID to him. This NSAID I'm talking about is legal and without prescription in my country but illegal in his country (it's an NSAID that's very harsh on the liver) but I never ever had a problem with customs about moving with this medicine.
Btw Australia is the harshest place to travel regarding customs checks, but if you don't tell anyone about your Bitcoin holdings, no one will know about it.