As of right now, Overwatch has no weapon skins, unless you count the gold coating that you receive for your weapons as a skin. However, that may be about to change soon- Reddit users good_samartian and Nyxxic have both noted evidence in the new Doomfist update videos for Overwatch that skins may be coming for all weapons very soon.
The evidence basically includes observation of the fact that characters have been spotted with weapons that are significantly different from the ones that they usually wield- this include Soldier 76’s rifle, as well as Sombra’s gun. None of these weapons are currently available in the game, even in the testing environment.
This seems to indicate that different skins for weapons for all characters in the game might be upcoming- maybe they will be introduced during the Summer Games event. We’ll have to wait and see, but I am sure news of more weapon skins won’t be treated negatively by anyone.