EnumWindows, EnumChildWindows를 이용해서 단추를 찾고 Click하는 방법을 사용하고
있네요... ^^

function EnumChildProc( phWnd : hWnd; poCaptions : TStrings ) : Boolean; stdcall;
var
  szFull : array[ 0..MAX_PATH ] of Char;
begin
  Result := phWnd <> 0;

  if Result = TRUE then
  begin
     GetWindowText( phWnd, szFull, SizeOf( szFull ) );

     if ( Pos( poCaptions[ 0 ], String( szFull ) ) > 0 ) AND
        ( poCaptions.IndexOfObject( TOBject( phWnd ) ) <  0 ) then
        poCaptions.AddObject( String( szFull ), TObject( phWnd ) );

     EnumChildWindows( phWnd, @EnumChildProc, LongInt( poCaptions ) );
  end;
end;

function ClickButton( ParentWindow : Hwnd; ButtonCaption : String ) : Boolean;
var
  lhWnd : hWnd;
  loCaptions : TStringList;
begin
  loCaptions := TStringList.Create;

  try
     loCaptions.AddObject( ButtonCaption, nil );

     EnumChildWindows( ParentWindow, @EnumChildProc, LongInt( loCaptions ) );

     lhWnd := 0;
     case loCaptions.Count of
        1 : ShowMessage( 'Window text not found.' );
        2 : lhWnd := hWnd( loCaptions.Objects[ 1 ] );
        else
           ShowMessage( 'Ambiguous text detected.' );
     end;
  finally
     loCaptions.Free;
  end;

  Result := lhWnd <> 0;
  if Result then
     PostMessage( lhWnd, BM_CLICK, 0, 0 );
end;