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To contract a selection, use select-modify-contract and select the number of pixels.
Again to smooth out the sky tones, you use the clone tool. Set a relatively large size, use a relatively low percent, select an area away from your problem area and then sweep the clone tool back and forth numerous times. You can select another area to clone from and repeat the sweaps. That should even out anything within a few seconds. Another option would be to select the sky, that should take only one or two clicks with the selection tool, then use blur-average. You may also need to contract and feather. You will then need to use the dodge tool set relatively low, say 10%, to lighten the sky selection towards the horizon. Again use a low selection and a large size and sweep numerous times so the effect is subtle and not detectable. Whenever you work on the sky, blurring is a good idea. Again, select, contract, feather and gaussian blur 2-4 pixels. If you make the right settings, the entire sky will blur but you will still have a clean sharp unblurred edge at the top of the mountains. Then when the sky is right, paste in the new moon. Personally I would leave the lightness in the sky around the moon and just get rid of the heavy glare just around the old moon. The diffuse lightness in the sky will help give the moon a natural appearance. It is easy to remove as I explained but much tougher to add that lightness back in if for example you were adding a moon to a sky that did not have a moon. Finally that noise and graininess you see in the sky is mostly a sign of being too much of a pixel peeper. The grain has to be pretty bad to show in a print since it will just disappear due to the printing process and dithering.