Safe way to unclip internal power wire?

Sadly, the connector shown is not what Apple used for the power button connector. There is no lip at the front part of the connector as the vid implies you need to lift. Here the cable side needs to be lifted ever so slightly to clear the connector shell and then drawing it the rest of the way out at an angle.

To better see here's the connector in the connected condition. Note there is no lip at the front end to grab. While hard to tell the silver springs at the backside is what presses in on to the cables connector side to hold it.

Now looking at the cable disconnected we can see the contact blades which need to slide out to clear fully

As to a better way to disconnect this connector, I use the knife side of the Halberd Spudger to lift from the backside under the wires entry, then I gently pull on the cable at an angle. Most people are too rough and pull the cable not realizing there's a bit of a latch here and body and the contacts need to clear before you can pull on the cable

And yes it's not as easy as it should be! These are designed for auto insertion machines not people!