Don't use in-camera white balance. Have the camera produce a raw file, then you take it from there.

You can measure the white balance of your sensor ahead of time, then use that correction for the star image. For something like stars, I'd use sunlight as the white reference. Put another way, sun-like stars will appear white and other stars will have colors relative to that. I have measured my sensor on a white target illuminated by direct sunlight. You can use a gray scale card to get various brightnesses, or do different exposures of the same sunlit white target. Either way you get curves for how each color in your sensor responds to light.

I've done this with several camera sensors and found them all to be quite linear. Given that, you only need to make a single white measurement since the same color balance correction applies to the whole dark to light range.

One thing to watch out for with stars is that they are point light sources and therefore could be focused so small that they hit a small number of sensels, which probably aren't balanced to red/grn/blu content. Put another way, if a star is focused on a single green sensel, then the star will appear green regardless of its actual color. The anti-aliasing filter over your sensor should help somewhat with this, but these filters still let some frequencies that will alias thru.