I've successfully sharpened cheap scissors with this knife sharpener I got marked down to $5.00 at Aldi a few years ago. I got a blunt pair I was using to cut sandpaper sheets back to cutting cloth again.
It doesn't leave the best finish on the scissor blades but it works well.

It's also made a cheap Chinese kitchen knife that was previously hopeless, sharp enough to slice a tomato cleanly.

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Ahh, if only victa had kept producing the thumblatch catcher series, they would be in better shape today!