Can you not uninstall the app? Note that there are 2 different ways to get apps installed. The traditional way is with an installer so going to Apps & Programs would cause it to show up. However it is possible you have the MS Store version. In that case right click the icon for the program on the Start Screen and Uninstall should be an option. Alternatively under Apps & Programs should be the list of store apps that are installed and you should be able to remove it from there.
If it was installed as part of an Office Deployment Toolkit deploy then it might be harder, in my experience. Ideally you should remove it from the ODT manifest before installing it in the future. I don't know if you can uninstall Skype without uninstalling Office if you installed it using ODT.
If you cannot uninstall it then you should just remove it from the many different places it may be configured to run from. The easiest solution in my opinion is to get Autoruns and run it as an Admin. Then look under the Startup tab for all the apps that auto-start. Find Skype and delete it. Then start Skype up and refresh the autoruns UI. If it shows back up then it is auto-adding it when you start so disable Skype by unchecking the box instead of deleting it. In most cases this prevents the app from adding its entry back but in some cases it doesn't work.