Nah, no need to do all that cutting. See the pics ? Now, there are little tabs on the metal pins inside the 4 pin connector. You need to push those in to swap wires around. I use a straight pin to push between the plastic and the metal pin.
You need to swap the wires around such that the black wire that runs to the fan gets its power from the 5 v + (usu. red) wire from the power supply.
Now, be careful with this. If you only rewire one of the 4 pin connectors, anything you plug into the other end of that 4 pin connector would be getting the wrong voltages and fry. If you rewire both ends (such that the colors get switched around but all the voltages pass through just like when you started - IE: As far as power draw is concerned, you only change around the wires that power the 3 pin fan connector) then you can still use that end of the connector (and you don't have to worry about accidentally frying stuff).