You need a 5~5.5 inch parabolic or shield cutter. Now what you do is raise the feather inside the cutter so the feather doesn't get cut to the full size. Using a 5.5 inch cutter, instead of a 140mm long and 16mm high fletch you'll get a 110mm long and 9mm high fletch which is perfect for Korean arrows.
"The fletches above were all cut with a 4" parabolic blade by adjusting the base plate for height and length." from http://herbsarchery.com/herbsfeathercutter.html shows what I mean
If cutting feathers with scissors, taping the feathers with drafting tape makes them much stiffer and easier to cut. Alternatively you can heat up a hacksaw blade over a stove and use it to burn the feathers to shape.
Also if you're going to be cutting/burning feathers by hand, don't use turkey fletches. They're expensive and honestly don't look or feel very good. Get some pheasant feathers instead and strip the feathers yourself. You end up with a much thinner stem/quill and the feathers just look better overall