Store some sats on an OpenDime.

If someone trust you enough, you can send the signed transaction data to the other person and they can broadcast it later when they get access to a connected bitcoin node. You could even just write down the seed phrase, put a certain amount of sats on there and give that to whomever you want to pay.

Mesh networks where one or more participants has a node that's able to broadcast the transaction for you could also be possible.

You could broadcast the TX over satellite too, e.g. with Blockstream Satellite. Or via radio.

All these options require some kind of preparing before the actual event, there is no way around it. If nothing is prepared, you'd just have to give out your existing seed/private key which is already settled on the blockchain.

If the blackout is caused by a major catastrophic event, I guess we don't care about money. Water, food, ammo and guns would probably be more important to stay alive.