To overlay the new sky on top of the old, start the Transformation -> Composite
dialog, put the bad-sky image in as the input image, the good sky image in as the
Overlay image, and associate the mask you made before with the input image.

You apply the mask by clicking on the white rectangle to the right of the amount
slider, and selecting the mask from the popup menu. The "Operation" field is set
to Blend, and Alignment to None. Overlay amount to 100%. The master white slider is at
100%, and the master black slider is at 0%.

Click the box that shows a preview.

The next image shows what I get when I hit "OK" at the top of the dialog.