Have not done this for pictures in this database, but for personal prints, there are a couple of techniques I've used in Photoshop.
One is through repeated use of the Lasso tool. I start in the sky close to the hard edges of the actual subject and select "feather" of about two pixels. I then carefully circumscribe the sky and make several adjustments.
1. If the noise has a color in common, you can unsaturate that color in your selected area but be careful not to change the whole color of the sky.
2. Blur, especially motion blur is useful. Blurring 2-3 pixels vertically and 10-20 horizontally can be effective. Even the "noise" filter tool is useful for this. Just be advised that the motion blur will pull in colors from outside the selected area if the range is set large enough.
3. Spraypainting with low opacity and low flow rates can be very effective but it takes practice. Use the eyedropper tool to select a local color and keep doing that over so as not to make the whole sky one color.
When the worst of it, the most hard-edged spots are gone, and being careful not to overprocess in the first pass, I will take the lasso tool again, this time with "feather" set to 6-8 pixels and draw another line just a bit farther out away from the subject edges and repeat the above steps or apply other corrective filters as needed. The key is subtlety - you don't have to get it all the way on the first pass.
You can repeat this five or six times and if you use a little care, the feathering of your selected area will prevent your repairs from being too obvious. I've taken a burned out and noisy sky in this manner and, using progressively more contrast brought out a really dramatic cloud base that could not even be seen in the original print.
Another is, with the lasso tool feathered no more than three pixels, select just the hard edges you need to retain for sharpness, then invert the selection and apply some global tools for softening or cleaning up the rest of the image. By tracing your lines with some accuracy here you can wind up with literally dozens of small areas of the picture deselected by a single use of the lasso tool.
For this database however, be mindful of the rules regarding manipulation of photos.
Happiness is not seeing another trite Ste. Maarten photo all week long.