Автор: http://www.swissdelphicenter.ch

{
  This code displays the application/file "Open With" dialog
  Passing the full file path and name as a parameter will cause the
  dialog to display the line "Click the program you want to use to open
  the file 'filename'".
}

uses
  ShellApi;

procedure OpenWith(FileName: string);
begin
  ShellExecute(Application.Handle, 'open', PChar('rundll32.exe'),
    PChar('shell32.dll,OpenAs_RunDLL ' + FileName), nil, SW_SHOWNORMAL);
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  if Opendialog1.Execute then
    OpenWith(Opendialog1.FileName);
end;