First, check the pin-out of the connectors on the new PSU cables and compare to the old PSU's cables. The pin-out may be different. If it is and the actual connectors are not different, reorder the sleeved cables to match the new PSU cables. If the connectors are different, swap the connectors. This is hard to describe, but would work as long as they have the same number of wires and the connector pins may be the same...I'd guess they are.
If you have to swap the PSU end connectors due to them being different or a different pin-out, what I'd then do is use the pin pusher to remove the pins from the new supplies connectors and the old supplies connectors one at a time making sure to keep the pin-out right to match the new PSU.
What you end up doing is using those cables you already sleeved. You have to be sure to do a pin-out layout for both to be sure you do it right, or POOF!

You should be okay with that having sleeved the cables and getting them back right. On my old Antec Modular and my current Corsair Modular the connectors are wired the same end to end, but the PSU end connector is shaped different between the cables. The pins are the same size, if wanted I'd just have to swap connectors to use my Antec cables on the Corsair.
Did I lose you?