Having never done this myself, you will have to take my advice with a grain of salt, but still...
I'm pretty sure that any semi-serious video-editing software (e.g. Adobe Premiere) will allow you to superimpose static images on a video stream. You'll just need to get a picture of the fretboard you like, edit it to get a transparent background in photoshop, and put it on the video.
You probably could do something fancier with After Effects, but it might be overkill tough.
Overall, it should be pretty trivial.
Edit: Just confirmed with a friend who does this for a living, and yes Premiere could do the job very easily.
Vincent