I really don't see any problem with paper wallets, hot/cold wallet on a phone, a seedphrase on a USD stick. I'm not sure where you're from, and I never seen this happening, so I really can't imagine them going through your phone apps. Is that even legal? Also, is this even something you have to do? I mean declaring your bitcoin holdings regardless of the amount?
Well, in the EU you must declare everything over 10.000€.
I would say that in general it is not legal for them to go though your apps but I have seen border control programs where it does seem mandatory, or at least they can make it more difficult for you to enter the country or hold you if you don't cooperate.
I was thinking hypothetically.
There are reports now of people getting stopped on US customs and being forced to decrypt their phones. Some journalists and researchers got apparently stopped and were told to handle customs their phones in search of any critisicms of Trump. That is some North Korea stuff. But laptops and phones being forced to be decrypted at airports are nothing new. There has been reports of this happening. For this, I wouldn't never cross any borders with anything encrypted. You simply cannot afford the risk that you need to decrypt your stuff and have your coins there. So simply upload your wallet somewhere in the cloud encrypted, then cross whatever borders and recover your backup and once you are safe to go then you could get rid of the cloud backup if you are not comfortable having your wallet online, but if it's fully encrypted then it's the same as trusting that SHA256 is not cracked so basically it's the same as trusting BTC addresses not being cracked.