OuterHtml Read-only in HTMLAgility Pack?

Why use the HTML Agility Pack if you're treating the whole document as a string. Instead look up tags and replace those then write back the document.

var doc = new HtmlDocument();
doc.LoadHtml(yourString); // or doc.Load(yourStream);

var links = doc.DocumentNode.Descendants("a");
foreach (var link in links)
{
    link.Parent.Replace(ConvertLink(link), link);
}
string newDocument = doc.DocumentNode.OuterHtml; // Or doc.Save();

And your ConvertLink would look like this:

public HtmlNode ConvertLink(HtmlNode aTag)
{
    var link = HtmlNode.Create("asp:HyperLink");
    link.Attributes.Add(...);
    return link;
}

(not compiled, so might need some tweaking).