Use the ShellApi function ExtractAssociatedIcon() to retrieve the icon that is associated with the file. Example:

uses ShellApi;
procedure TForm .Button Click(Sender: TObject);
var
  Icon : hIcon;
  IconIndex : word;
begin
  IconIndex :=  ;
  Icon := ExtractAssociatedIcon(HInstance,
                               Application.ExeName,
                               IconIndex);
 DrawIcon(Canvas.Handle,  0,  0, Icon);
end;