Is possible get Exception type in a switch statement without using ToString?

Question

I need to check the type of the exception in a switch case, and perform different tasks for a specific exception, what I did for the moment is create a method that will be called when an exception is throw, so:

private static void ShuntException(Exception ex)
{
    switch (ex.InnerException)
    {
        case System.Net.WebException:
            DoSomething();
            break;
    }
}

essentially the problem's that I get this error:

Error : 'WebException' is a 'type', which is not valid in the given context

I can fix this situation using GetType().ToString() and then writing the Exception type manually like so:

private static void ShuntException(Exception ex)
{
    switch (ex.InnerException.GetType().ToString())
    {
        case "System.Net.WebException":
            DoSomething();
            break;
    }
}

the last example that I added working well, but I prefer the first that doesn't working for the error displayed by the compiler, what I missing or I doing wrong?

Thanks for any help.