Decreasing an ATX PSU voltage using the sense wire?
I cannot see why connecting the 3.3V sense wire will have any affect on the 12V output. All it will do is try to pull the 3.3V output as low as possible, because the sense wire is feeding back 5V which tells the controller that the 3.3V output is over-voltage. It may even shut down the 3.3v output.

You could use a schottky diode in series with the 12V output. A good schottky will drop about 0.4V to give you 11.8V. What current do you need to draw from the power supply? You need to chose a schottky diode that is suitable for the current.