Forsyth Jones brings up a decent strategy, but to differ a bit from his suggestion you could just use GnuPG to encrypt a text file with the seed phrase in it, and store the encrypted file on a cloud server until you reach your destination.  You could also encrypt a passphrase the same way and store it in a different way, such as send it to yourself in a email that's operated by company other than the cloud service, or yet another cloud provider.

That way all you have to remember is the password for your PGP key, and you have nothing on your person or in your luggage that suggests you own bitcoin.

I would rather trust an open source solution such as GPG/PGP than a third party software or an entire OS on a USB stick, and again you wouldn't have anything with you that could prompt questions.