Yes, you need to amputate the entire plug - just cut off the cable as close to the plug as possible.
The transparent plastic ring goes around the connectors (solder connection points on the plug) once you're finished - so start off by threading the cable through the BLACK PLUG COVER, then thread the cable through the TRANSPARENT RING.
Then solder the wires to the plug. Once you've finished soldering and clamping the cable (not too tightly though), thread the transparent ring over the soldered connections, and finally screw the plug cover on.
If you want to go for a stronger connection, throw away the transparent ring and purchase some heat-shrink tubing - then cut off around 30-40mm of tubing - then just put that in the assembly process where the transparent tubing would be, but before screwing on the black cover, you need to shrink it with a hair dryer or a heat gun. It will shrink tightly over the connections and also serve to strengthen the end of the cable which normally needs some bracing to prevent quicker wear and tear.