You said you plan on using a constant current driver. That's the optimal way to run LEDs, and if you get the correct driver, you should be good to go on that point. What the driver does is to drop the voltage to 'whatever is necessary' to get the set current. If that's 2A, the driver will apply just enough voltage to get 2A in the LED. That voltage will vary a bit with temperature, from LED to LED, etc.
"The correct driver" will be one that can be set to the current you want, and can handle the range of input and output voltages you will give it. A switching driver, particularly a buck type (AKA step-down) should do that fairly efficiently. There are lots of these around, from a few bucks at DealExtreme, KaiDomain, or other catalog outputs, to $30-40 for top-end ones from Taskled.
I think the big problem you're going to have though is heat. If you put 12W into the LED, and the driver dissipates 2W, around 2.5-3W is going to come out the front as light, the rest will be turned into heat. The light is a plastic body, which isn't a great conductor of heat, so the air in the light will get pretty warm. The incandescent bulb can handle this without a heatsink, but the LED can't. And you probably can't fit a big enough heatsink into the light. The designers at Princeton Tec who built the Shockwave LED only chose around 4W of LED, almost certainly for this reason. And they had access to lots of money and if not seasoned LED designers, at the very least some decent engineering staff.