I cut off the top part.
Then I completely deconstructed the skirt and rebuilt it again (see blogpost here: http://saga-i-farver.blogspot.dk/2014/11/50ernederdel-til-skaternederdel.html?m=1 ).
I cut the zipper off with the fabric around it, the overlay and that [little piece of fabric with a buttonhole in it, at the top of zippers].
When I was about to separate the zipper from that fabric I wondered (out of laziness) I could just sew the whole thing on again.
And it worked! And i allowed me to preserve the overlay and the buttonhole-thing. It actually looks better than the bare zipper would have.
Finished shorter and waist-fitting skirt.