http://support.xbox.com/en-US/xbox-3...m/power-supply

AC power cords

The AC power cord is 1.8 meters (approximately 5 feet, 9 inches) long and is detachable from the power supply unit.

The end of the power cord that plugs into the PSU has two or three holes. The number of holes corresponds to the number of prongs on the PSU. You must use only the two-prong PSU with the cord that connects by using two holes and use only the three-prong PSU with the cord that connects by using three holes. If you use a power cord other than the cord that was designed for your PSU, you may damage your PSU or your Xbox 360 console.

The plug at the end of the power cord that connects to your electrical outlet can be one of several types. The plug type depends on the country and region where you purchased your console. See the following table for more information about the different plug types.
So the official line is, no, do not force a different cord to work. Whether that's true or just MS wanting you to buy your stuff from them, couldn't say. Don't think I'd risk it unless it was impossible to find a proper cord.