I have never seen a USB cable that did not use the same color code - leave it to Wyze to use a non-standard color code…
Looking at your second photo, it appears that the four wires are (top to bottom in the photo) White, Green, White, Red. It also appears that the outer White is maybe a larger wire size than the inner white. In every other USB cable I have seen, the larger White would be Black - as is your replacement cable. The Red and Black are normally 5V power (positive on Red). The white and green are data. So best guess is that the White and Green center two wires on the Wyze cord connect to the White and Green of the replacement cable. The Red connects to Red, and by process of elimination, the larger outer White on the Wyze cable connects to the Black on the replacement cable. That is my best guess.
One other note. I am NOT a fan of those solder connection butt splices you show. They are quick and easy, but result in a poor connection. In particular, there is no mechanical strength in the connection. In a proper soldered connection, the wires are twisted together sufficiently that they are solidly connected to each other before adding the solder. And the wires are heated enough to melt the solder. With those splices, the wires start somewhere in the neighborhood of each other with no mechanical connection, and the solder melts over essentially cold wires. Not a good joint.