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The other way of doing this is by using a multimeter to trace the existing cable and write it down then trace the new cables and write them down.
Now on both plugs old type and new, you should be able to press the retaining clips in on the contacts and be able to pull the individual contacts out then swap them around according to your drawing, and as long as you have got everything correct it will work.
I've done this before without any problems.
Just take your time and double check your tracing of the wiring.
Dont wory if you don't have a screen wire, not all usb plugs do.
Now on both plugs old type and new, you should be able to press the retaining clips in on the contacts and be able to pull the individual contacts out then swap them around according to your drawing, and as long as you have got everything correct it will work.
I've done this before without any problems.
Just take your time and double check your tracing of the wiring.
Dont wory if you don't have a screen wire, not all usb plugs do.