Okay. I left the fix of the left side of the chain. The right hand doesn't seem to be bugged, but it's better not to risk anymore.
Flagrum is bugged for me, so I can't use it to solve the issue of the skin's appearance in the shadow.

One more time to the old normal version to compare the hands.

Tried to fix the chain on the left side. I just need to fix such a noticeable bug. Well, it seems not bad.

The normal version again, without fixes of some body's parts, but it's better than where the right hand started to turn into the bugged one. It's like Flagrum is infecting Mod Organizer more and more with every new fix.

Fixed a gap on the right shoulder, but the right hand has become more black.

Fixed some body parts and tested the mod, but the right hand has become a little bit black.

The normal mod here. I understand now. I deleted the mod from Flagrum then it was bugging with endless uploading (when I decided to try several times) -> there were no any uploaded mod, but Flagrum is connected with Mod Organizer somehow (my normal mod is here). Wow... then I saw the mod uploaded with Mod Organizer in Flagrum... I can't delete it in Flagrum 'cause it's possible it will be deleted from Steam too. O.O

A test of that mod with the bugged hand.

Finally. The hand's bug is gone, Noct is fine. Wait! Smth else is gone... oh, my nerve cells. ̶T̶h̶e̶ ̶b̶u̶g̶g̶e̶d̶ ̶o̶n̶e̶ ̶i̶s̶ ̶s̶t̶i̶l̶l̶ ̶h̶e̶r̶e̶.̶

Updated the name of the file in the game, but the game didn't update it or Mod Organizer was bugging.