How Do You Dynamically Change The Colors of a Flattened Image?

Im inexperienced with working with raster graphics and I can do simple stuff but I have no idea how to do this. I have to separate this graphic to print on t shirts, and the program I have will only separate it well if the colors are exactly RGB "Orange" and RGB "Blue" If the color is off the separation will be dull and not vibrant. So what I need to do is take this flat raster image a client sent and select all of the orage-ish and blue-ish colors to make them closer to the pure RGB color. Hope that makes sense.

Heres the image so you have a better idea of what Im trying to do:

The image is quite pixelated and not very high res, so it will make selecting difficult I think...