I had the same problem after upgrading today. The error affected only the external display for my laptop. Microsoft Support took over my PC and after a rather long trial and error session came up with a solution: Upgrade the graphics driver(s) to the latest version:

Device manager -> Display adapters -> (select adapter) -> Update -> Online search

Display: Acer S240HL. Adapters: Intel UHD Graphics 620 and NVIDA GeForce 940MX I am uncertain if they updated one or both.

Preventing the classic Skype application from starting

With the classic Skype application window open, do the following:

1. Navigate to Tools > Options.
2. Highlight the General settings section on the upper-left.
3. Uncheck the option to Start Skype when I start Windows on the right.
4. Click the Save button.

Preventing Skype for Windows 10 (Skype UWP) from starting

On the other hand, if this is the Skype UWP app those options won't be available. Based upon a similar question on the Microsoft Answers web page, their Skype Community Moderator explained what needs to be done:

The new Microsoft Skype for Windows 10 (Skype UWP) application has never been present in the Startup tab. Windows apps are not managed the same way as a Win32 application. The classic Skype for Windows Desktop is a Win32 application, Skype UWP is not.

If you close your computer without signing out of the Skype UWP application, then on next computer boot, Skype will auto run in the background. To maximize Skype UWP you will just need to click on the application icon.

If you prefer not to be signed in automatically on Skype for Windows 10, you can sign out from the app. We won't sign you in automatically after that.

In other words, Skype UWP users simply need to logoff from within the app to prevent it from starting automatically during a subsequent Windows 10 login.

As a potentially viable alternative to the Skype Community Moderator's advice, you can turn off the background app functionality for Skype. Navigate to the following location:

Start > Settings > Privacy  

Ensure that you have selected Background apps on the left-hand side, scroll down on the right until you find the entry for Skype and change the slider to Off.

That being said, in addition to the obvious advantages there are minor drawbacks to using this method:

Bear in mind that there’s a downside to this. If you prevent the Alarms app from running in the background, for example, any alarms you set won’t go off. If you prevent the Mail app from running in the background, it won’t notify you of new emails. Apps normally run in the background to update their live tiles, download new data, and receive notifications. If you want an app to continue performing these functions, you should allow it to continue running in the background. If you don’t care, feel free to prevent the app from running in the background. You can still use the app normally, but you may have to wait for it to fetch new data after you launch it.

Uninstalling the classic Skype application

Taking it a step further, if you want remove the application entirely, the classic Skype Win32 application will be listed within the Programs and Features applet in the Control Panel. Simply highlight the Skype entry in the Name column and select the Uninstall button near the top.

Uninstalling Skype for Windows 10 (Skype UWP)

In contrast, the Skype UWP app won't be found in Programs and Features. As a result, if you want remove that particular version, navigate to the following location:

Start > Settings > Apps  

Ensure that you have selected Apps & features on the upper-left, scroll down on the right and left-click Skype to select Uninstall.

Notably, if the Skype UWP application is already running, before attempting the Uninstall you may need to first select Advanced options, then choose Terminate to "Immediately terminate this app and its related processes." After that, select Uninstall as desired.

Additional reading: Download Skype for More Features Than Windows 10’s Built-In Version