Okay, after searching the web for hours I think,
NOBODY knows an answer to this question, so I wrote
my own code, here it is (only tested on WinXP using
IE6)

first a function, that finds the default app for any File extension: 
#include<Registry.hpp>
AnsiString GetDefaultApp(AnsiString ext)
   {
   TRegistry* reg = new(TRegistry);
   reg->RootKey = HKEY_CURRENT_USER;
   if(!reg->OpenKeyReadOnly("Software\\Microsoft\\Windows\\CurrentVersion\\Explorer\\FileExts\\."+ext+"\\OpenWithList"))
      return(NULL);
   try
      {
      AnsiString MRUList = reg->ReadString("MRUList");
      AnsiString ret = reg->ReadString(AnsiString(char(MRUList[1])));
      return(ret);
      }
   catch(...)
      {
      return(NULL);
      }
   }

I also wrote a code that finds the whole OpenWithList (the first
item in the List is the default app...) 
#include<Registry.hpp>
TStringList* OpenWithList(AnsiString ext)
   {
   TRegistry* reg = new(TRegistry);
   TStringList* ret = new(TStringList);
   reg->RootKey = HKEY_CURRENT_USER;
   if(!reg->OpenKeyReadOnly("Software\\Microsoft\\Windows\\CurrentVersion\\Explorer\\FileExts\\."+ext+"\\OpenWithList"))
      return(NULL);
   try{
      AnsiString MRUList = reg->ReadString("MRUList");
      for(int i = MRUList.Length(); i > 0; i--)
         ret->Insert(0,reg->ReadString(AnsiString(char(MRUList[i]))));
      return(ret);
      }
   catch(...)
      {
      return(NULL);
      }
   }

now the code to launch the default app for html files and giving
the URL as parameter: 
#include<shellapi>
void OpenURL(AnsiString URL)
   {
   AnsiString app = GetDefaultApp("html");
   if(app == NULL)
      return;
   ShellExecute(NULL,"open",app.c_str(),URL.c_str(),NULL,SW_SHOWDEFAULT);
   }

Now you can open a URL in a new Browser using this command: 
OpenURL("http://www.AlgorithMan.de/");

CU

AlgorithMan