I have done exactly what you are doing. You have two options. The first is to remove the transformer in the hood that runs the leds, wire the ac side to an standard wall plug(make sure to ground to the chassis) and the dc side to the leds. The second is to buy a 12v dc transformer walwart and wire it into the leds. The leds should be wired in parallel to either transformer.
I did the second, but used a variable output walwart so I could adjust how bright the leds were. Check ebay for walwarts they are super cheap. Rat Shack is not so cheap. Who cares if the voltage varies a touch and they might not last six lifetimes? They are for moonlights!
BTW You can cut that connector off and soldier or use wirenuts to make the need connections.
Well I think I just said what Ping did only less concise. Great!