Wiring a Micro-USB cable that doesn't have a black GND and has 3 unshielded wires?
Putting on a new connector is generally not worthwhile - even if you get the connectivity correct, it is hard to do it in a way that will be durable and lasting.
If you really want to do it though, the only truly reliable method for figuring out your puzzle is to go a continuity test from the intact end of the cable - eg, plug that end into USB socket, get a credible reference of the USB pinout, and figure out which signal is which.
If the other end is not standard USB (eg, unique product connector) you might have to do the test with the remains of the cut off end.  Generally though a non-standard cable would have its non-standardness on the end you are trying to replace, and the remaining end would be a standard USB &quot;A&quot; plug.
Don't trust the colors, they've been known to be wrong in manufactured cables - there's no real expectation that anyone would ever cut a manufactured cable and try to join it to something else.