You can hook up your own download manager that is effective only in your webbrowser control host process by implementing IServiceProvider in the control site and implement QueryService to return an IDownloadManager object when asked by the webbrowser control
In Windows Form's Webbrowser class, a control site is created for you by default, but you can override the control site by create your own WebBrowserSiteBase class and override the WebBrowser.CreateWebBrowserSiteBase Method. There is no such extensibility if you use the webbrowser control from WPF, Silverlight or Windows Phone.
I suggest you write the download manager in C++ due to the amount of interop required if you code in C#. There's an example for a C# webbrowser control using a native download manager here.