It's great that you've found a workaround
If you want to fix your issue, I believe I've found the solution. Repeat the above instructions to launch an elevated command prompt, and use this command: takeown /f C:\programdata\skype\apps\login
Then use this command: del /f /q C:\programdata\skype\apps\login
Then uninstall Skype.
I, wrongly, thought this was a permissions issue on the file when in fact, it's an issue with the folder.
But if you're happy with the portable version, then feel free to stick with that - whatever works best for you