It's important to clarify the terminology you're using:

Cold storage refers safer storage which is typically access infrequently and at some inconvenience.

Multi-signature is the requirement of more than one signature to spend.

Air-gap means the hardware making signatures is not connected to the internet.

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Not being signed in anywhere doesn't help you if you enter your seed phrase on a hacked machine.

I'm concerned that you're willing to trust a wallet provider... who are you talking about in that case, for example?

12 words might not be that hard, but songs are fun and meaningful and seed words are often nonsense.