Im not really sure what Webkit has to do if your wanting to download the html of a page in C# as you can do that using HttpWebRequest class.
See sample below, it will download the html and "permanently" save it to a file:
WebRequest req = HttpWebRequest.Create("http://codeproject.com");
req.Method = "GET";
string htmlstring;
using (StreamReader reader = new StreamReader(req.GetResponse().GetResponseStream()))
{
htmlstring = reader.ReadToEnd();
}
using (StreamWriter outfile = new StreamWriter(@"c:\temp\websitehtml.html"))
{
outfile.Write(htmlstring);
}