This is an extension to the XAML WebView for invoking scripts from a ViewModel

ScriptInvokeWebViewExtensions.cs

public static class WebViewExtensions
{
    /// <summary>
    /// Using a DependencyProperty as the backing store for Content Uri.  This binding Content Uri.
    /// </summary>

    public static readonly DependencyProperty InvokeScriptProperty = DependencyProperty.RegisterAttached(
        "InvokeScript",
        typeof(string),
        typeof(WebViewExtensions),
        new PropertyMetadata(String.Empty, OnInvokeScriptChanged));


    /// <summary>
    /// Gets Uri source associated with the <see cref="WebView"/>
    /// </summary>
    /// <param name="obj">The <see cref="DependencyObject"/> that has the content uri.</param>
    /// <returns>HTML content</returns>
    public static string GetInvokeScript(DependencyObject obj)
    {
        return (string)obj.GetValue(InvokeScriptProperty);
    }

    /// <summary>
    /// Sets HTML from the <see cref="WebView"/>
    /// </summary>
    /// <param name="obj">The <see cref="DependencyObject"/> that content uri is being set to.</param>
    /// <param name="value">HTML content</param>

    public static void SetInvokeScript(DependencyObject obj, string value)
    {
        obj.SetValue(InvokeScriptProperty, value);
    }

    private static void OnInvokeScriptChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
    {
        WebView wv = d as WebView;
        var script = e.NewValue as string;
        if (script == null)
        {
            return;
        }
        wv?.InvokeScriptAsync("eval", new string[] { script });
    }
}