Change to the core database
Go to: /sitecore/content/Applications/Content Editor/Context Menues/Default
Duplicate the item Insert (Or any other of template "/sitecore/templates/System/Menus/Menu item". I recommend copying, as this template is not in the "insert options".
Rename the new item as "Publish"
Change the field display name to "Publish"
Set the Icon field to "Office/16x16/publish.png"
Set the Message field to: item:publish(id=$Target)
Change the Item icon to "Office/16x16/publish.png"
Now, to avoid disappointments, in scenario where user may think that they can publish, to later found out they can’t, we have to apply security:
With this settings, only user with the role “Sitecore client Publishing” can see this button. This is the same security as applied to the default button.
To be fair, I have to give the credits to Benjamin Vangansewinkel and his post, who gave me the idea. I just added the icons to make it look nicer...
That's it, now you should get something like this:
Now run to show it to your experienced Sitecore users and watch their faces of joy!