I actually wouldn't describe what you're seeing as a halo artifact. It seems to me to be posterization — there just aren't enough tones to smoothly represent the gradient of the sky. It just happens to be in a circular pattern because in this image the center is brighter and then diminishes evenly in all directions. In a different image, this same effect might appear as horizontal or arcing bands.

If you look closely, the banding is actually present in the first image as well, but the noise provides a sort of dithering which masks it.

You could probably reduce this by using an all 16-bit workflow (RAW to TIFF instead of JPEG) but if you end display will be normal computer monitors, that's not much help.

So, general solutions are:

• Leave the noise; it's not that bad. (Or, apply high NR to the area around the plane, but leave the rest of the image alone — see Darktable: masks.)
• Introduce artificial grain/dithering, which will have the same smoothing effect and may appear less annoying to you. In fact, you might want to do this even in addition to the above, because as I mentioned, if you look closely, the artifact is apparent even in your first (non-denoised) image. You can do this by enabling Darktable's dithering module.
• Increase the recorded exposure significantly so the sky is a brighter blue. There are more tones to choose from in the brighter keys, and then you can "stretch" these across the sky with less banding. *

In this particular case, you have another option, since the sky is featureless: get rid of the vignetting, and just replace it with a flat blue color taken from that right around the airplane:

You could then add back slight vignetting artificially, taking care to avoid any banding.

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* This applies to exposure when capturing the image. The human response to light is non-linear; twice the light only appears a small amount brighter — but is a significant increase in the data recorded. This gives you more room to "stretch" those values over a broader final range. Many newer and higher-end cameras have 14-bit RAW conversion, which makes this less of an issue, but the D40 has only 12-bit conversion, so it can matter in difficult situations.