The funds are not in your phone, so you aren't doing anything ilegal.
If you have a credit card with a $20.000 limit, would you be doing an ilegal thing taking the card with you during the trip?
My advice is to turn off the phone and refuse to turn it on.
I agree that there is no bitcoin on the phone, its just a signing device.
As for just not turning on the phone... I think that's a pretty naive take. They can confiscate the device and hold you in jail because its the law.
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