Вы можете легко подключить XmlTextWriter к StringWriter, а затем отправить полученную строку в браузер:
StringWriter stringWriter = new StringWriter();
XmlTextWriter xmlTextWriter = new XmlTextWriter(stringWriter);
// write your transform to xmlTextWriter...
xmlTextWriter.Flush();
xmlTextWriter.Close();
stringWriter.Flush();
string result = stringWriter.ToString();