It's not the screw, I have very expensive hair cutting scissors. The cost of some of these Japanese and German scissors was in the 200-600 dollar range, back 20 yrs ago. Some are cobalt, "1 drop and they are done". so I always used to have a "guy", every good salon, had a Guy, who would come in once or so a month and sharpen them, Back in the 80's -2000, the cost went from $15-$40.00 per pair, to do them right. It is a cottage industry with all sorts of special machines and courses being given for thousands of dollars.
If you google it you will see, there are all kinds of gizmos for sale to sharpen those expensive scissors. But I remember a little Italian guy with a file, who did as good a job as any of the fancy machines did, and I think that they can be done by hand, "having run one over a water stone, one time, and it actually worked. But I am not brave enough to attempt it again, having read how hard it is supposed to be.
Many of those machines actually say, not for hair cutting shears. Here is a link just to show how expensive they are and why these guys get so much to sharpen them.
http://www.mysalontools.com/5-5-kam...jl-d7ChQsqLv5DUDL2KEWs5_lzZyBF4KtnBoCyjHw_wcB.
I figure if you can sharpen those, you can sharpen anything.