Yes, this is easy if you have a good ICC profile creation tool like i1Profiler and a color checker shot with your camera.
Step one: Create an ICC profile from the color checker data and use the current light source condition as the illuminant for your profiles white point..
Step 2: Create another profile with the color checker and the new illuminant. (e.g. mercury or sodium street lamp) Since it's not a standard Illuminant. You will have to plug in your trusty i1Pro2 or ColorMunki and go out and measure the light source you want your images to use.
Step 3: Now you have the record of the data for both illuminants built into profiles. Since what you want is for your images to have that casted look of a different white balance, so to do that you convert to the first profile with the correct white point. This should keep the colors the same on screen, then simply assign the new profile. That will show you what your image would look like under the new illuminant. If you like what you see then convert from that new profile back into a standard color space like Adobe98 or sRGB so you can share print or post it.