If the camera was effectively in daylight white balance at the time the shots where taken, then you can deduce the color shift that happened, and apply it's reverse to the image. Specially if you have the raw files. JPEG would work too, to a lesser extent.
For simplicity lets say that every sensor has it's own deviation from "correct" color, due mainly to design, materials and manufacture. The camera software somewhat applies a correction profile to reproduce color as best as possible. It does that in any WB setting, using different "shift values" for each light source. In principle, "daylight" setting assumes "white" light (uniform intensity for all light frequencies across visible spectrum) is illuminating the scene, so it should not shift color in any way, except to compensate design limitations in the sensor. That shift would be, in any case, the best compromise in which the designers settled for you particular make and model (and firmware) of camera.
My idea is that if you take another picture with the very same settings (particularly white balance), same lens, as your moon shots and then evaluate it straight out of the camera, using a correctly calibrated monitor, you should be able to work out what changes the image needs to better represent the actual scene. These changes should, theoretically, render a good result when applied to the images that you need to correct (the moon shots).
By changes I mean, for example, + 200 points in color temperature, 7 points towards green in green/magenta, etc.
An editor like Lightroom or Adobe Camera Raw is very helpful for this as it allows you to copy and paste the color settings of the sample shot to the moon shots. In other photo editors I take note of the values in any color/contrast/hue/saturation, curves/levels/etc (Not very efficient).
A crude calibration of your camera
To further know about the color shifts that your camera may be applying, even in "daylight" white balance, I suggest the exercise of photographing different lightsources against a black non reflective (or very distant) background. They may be light bulbs (incandescent, fluorescent and/or LED). Nothing fancy, use what you have at home, even some car headlamps may do.
Take direct shots at these sources while minimizing the influence of any others. Evaluate the shots in your editor+monitor and work out whether your camera shifts towards red, green or blue. The differences may be very subtle, but hopefully you'll learn how your camera behaves. Generally, when you underexpose a direct shot of a light source, it's color cast becomes more apparent, almost like if you augmented the saturation in your editor.
Also, check if you had any special profiles in use. For example my camera has "Natural", "Vivid", "Muted" profiles. They affect the color of the image. When I import into Lightroom, by default it applies "Adobe Standard" profile. None of the profiles renders the same result as other.
Most cameras have such profiles or color modes, with different names and they are often customizable and may have color shifting settings.
Anything that could have been on the atmosphere between your camera and the moon can affect the perceived color of it. Besides the well known red shift that occurs near the horizon, water vapour, suspended particles, etc. may also distort the color of an image. Light pollution is in part, light from cities bouncing, reflecting, and refracting off those vapors and particles.
A couple of anecdotes on perception
However, you will be limited by your own perception at the time of capture, and your own memory. Consider the following anecdotes.
Night vision/low light sensitivity of the eye: I had been on a beach, at night for at least 4 hours, in a remote location very far from any artificial light sources. My eyes' got so adapted to darkness that kind of had my eyes in "black and white mode" (Read on cones and rods related to eye light sensitivity for information on how this happens). My surprise was when I downloaded my captures to the computer an all of them had color. I could not recall any color in the scene, I had to trust the camera's output.
Color sensitivity of the eye: I have an issue with streetlights. In my country, there are two commonly pressurized gas lamps in the streets. In photographs they show as either orange or green. I assure you, that I see only orange or blue lights, my eyes do not register them as green. I do not know why that happens but it seems to affect me only with street lights...
Consider also that our ability to recall exact colors, tonalities, light intensities from a scene is limited. Even our emotional response to the scene may cause our memory to recall a more/less colorful scene than what was recorded. And, if, at the moment we thought, for example, "this photo is less colorful than the real object", over time we recall that phrase or idea, and may end up cranking the saturation too much up, more than necessary.