The question is, in what depth does the search go to? I mean, do they scrutinize your objects (& devices) or do they just do an ordinary check?
In hard secondary (i.e. if you are evasive during the interrogation) they do a full forensic search of the hard drives of your computers and the storage mediums of your other devices.
So if they find anything related to private keys on there then you are probably cooked.
What I would do, is write the seed phrase inside a notebook on a random page, preferably one that has some other manuscript on it, and then it would arouse less suspicion from customs and border protection or another agency.