Lovely fabric.
Thanks for the pic, yes I wanted to see a pic of the skirt you wanted to alter rather than a pic of one online.
Is it lined? Does it have two side seams and a back seam or just two side seams as you said there was a size zip in the skirt? If it's not lined and has two side seams only (with zip) then I would proceed as follows-
On a normal size chart the difference between RTW from a size 16 to a size 18 appears to be 3 inches at the waist and 3 inches at the hips? Is that what you were thinking of reducing it by i.e. one and a half inches on each side, if there are just two side seams in the skirt?
If so, you will need to unpick both side seams and zip and reinsert the zip and side seams? It looks as if the waist has a facing to it? If so, you would need to unpick it only at the seams rather than take all the waist facing off.
size 16 33 85 43 108.5
size 18 36 92.5 46 116