Solution
The NI Web Server does not provide any functionality for checking the list of deployed web services. You would have to manually check the file system on disk, as each web service will have an INI file in C:\Program Files\National Instruments\Shared\Web Services\NI\_lightweight.
You can use your command prompt terminal to generate a list by using the following command -
dir /s/b "C:\Program Files\National Instruments\Shared\Web Services\NI\_lightweight\*.ini
If your web services were installed via packages, you might also check the NI Package Manager for installed services.