The suggestion is that if Skype can be opened but using the link isn't working then edit the link so it can find the skype programme in order for it to run.
If you right click on the icon and select properties that will usually bring up a load of tabs to select from.
The default tab shown is "Shortcut" and will have boxes such as "Target" which must show/define the path on your drive and the skype programme file. *Possibly* "C:\Program Files (x86)\Skype\Phone\Skype.exe"
And "Start In" which is usual the same path minus the programme filename. *Possibly* "C:\Program Files (x86)\Skype\".
If you ensure these are correct and will allow the icon to find the programme it is supposed to start. You can then OK your changes and try the icon again.
Might be wise to note what you have changed from, somewhere first, in case it doesn't go to plan and you want to put it back as it was.