Our local fly fishing shop asked me to sharpen scissors including their very small (1 inch long) craft scissors used to repetedly cut filament fishing lines.
These blades are hooked to the side (not curved such as lopping shears) and they complain that their nicest tools dull easily. I'm interested in determining if we have a way to sharpen these scissors.
Sharpening is important but also consider Tungsten Carbide scissors. You can buy them from Amazon nowadays. I have many years of experience using tungsten carbide scissors and some of my scissors are 20 years old and still sharp. Of course, I was cutting catgut lines and not filament.
Some tungsten carbide scissors are only $16 at Amazon.
I don't know if this helps or not, but maybe you could clamp the scissors by the handles in the scissors jig? With such a short blade something like that might work. Just depends on if you can get the bevel to contact the wheel at a consistant angle.
Could you sort of freehand it with assistance of the scissors jig for stability? Slightly rock the top half on the sides of the jig whilst maintaining contact with the base to maintain angle? Maybe just freehand them? I'd experiment. Clamp them in the jig and see if anything makes sense.
Rhino might be on the right track. Unless hooked blades are absolutely necessary for the task, maybe short straight blades that could be easily sharpened or Tungsten Carbide scissors that maintain and edge longer might be their ultimate solution.
As you can probably tell, I don't know what I'm talking about and just taking pot-shots here, but hopefully some useful ideas.