If multi-texturing is supported, texture coordinate generation will affect the active texture unit (quote from the documentation, emphasis is mine):
When the ARB_multitexture extension is supported, glTexGen sets the texture generation parameters for the currently active texture unit, selected with glActiveTexture.
So you simply need to make sure texture coordinates generation is disabled for the color texture, but enabled for the shadow texture. As you guessed, this is done with
glActiveTexture(), by writing for example:
glActiveTexture(GL_TEXTURE0); // Assuming the color texture to be #0
glActiveTexture(GL_TEXTURE1); // Assuming the shadow texture to be #1
glTexGeni(GL_S, GL_TEXTURE_GEN_MODE, GL_EYE_LINEAR);
glTexGenfv(GL_S, GL_EYE_PLANE, textureMatrix.GetRow(0));
This being said, you're adding to yourself a lot of trouble by sticking with fixed pipeline instead of using GLSL.