I think there are some lightguns made now that will work with an LCD. I'm sure it would be easier to adapt that for use on the NES than to take an entirely different piece of technology and use that.
Plus, the x/y value idea with an arduino sounds like it would work, but that's not how data goes into the NES. How would you get info about where the targets are on-screen to the arduino? Remember, all the information that the lightgun sends to the NES is "I see white", or "I don't see white" (with some shades of gray for multiple targets). Not x/y data.