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.
I have been into security checks on a lot of countries and I don't think they never searched anything inside the phone, so I guess it's safe to carry the seeds in digital format like in a separate mobile that's never connected to internet.
Or you can create new wallet and fund the amount you needed then upload the seed in a cloud by this they will not have a clue of it.
We only responsible to disclose we're bringing physical items like gold or cash and no need to disclose about our digital assets.
Same, never heard of anyone having their phone searched at airport.
Even then, you should have your shit under password, 2FA, encryption, don't have your shit saved in a NOTE, and then a shortcut on your home screen.
What if you lose your phone, or it gets stolen, it's relatively easy to unlock it, so don't put your shit out in the open.
Thief most likely won't find something you've put in some XY folder, but will most definitely check your pictures, google drive/keep, other popular apps he can access, also will probably go after list of everything in your Authy :/
Making me think of it, does anyone have general suggestions for phone security? Maybe a kill switch? This way if your phone get seized by customs authorities or any other thief, you can just destroy it's contect instead...