I sort of figured out something that could work for this by accident once.

With Graphics Gale(it's free, so it's worth trying) you would first create a new blank file, and put the colors from palette 2 on the blank page, and save it as a .gif file.

This will save the palette of that file to whatever colors were in the image (your second palette). Whatever you copy onto that image now will only be able to use the colors saved to it's file, and it will automatically change the colors of the copied image to the closest match from the palette saved to that image.

All in all, it should only take 5 minutes or so to figure it out and do it, but if you need me to, I can make a picture guide to help.