Just cut off the connector from the old power supply and adjust it on the new one while preserving the color code. But if you want to be 100% sure for the polarization use a multimeter to determine the positive and negative wires.
It's not absolutely necessary to use soldering iron , you can just twist the wires and isolate them with heat shrinking tubes.
Another way is to change the entire cable from inside the PSU with the cable from the old PSU. But here you'll need some soldering skills (it's not that hard).
Hope it helps.





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