Просто используйте событие ContextPopup и имитируйте щелчок левой кнопкой мыши
type
TForm1 = class(TForm)
edtRich: TRichEdit;
procedure edtRichContextPopup(Sender: TObject; MousePos: TPoint; var Handled: Boolean);
end;
implementation
procedure TForm1.edtRichContextPopup(Sender: TObject; MousePos: TPoint;
var Handled: Boolean);
begin
mouse_event(MOUSEEVENTF_ABSOLUTE or MOUSEEVENTF_LEFTDOWN,
MousePos.x, MousePos.y, 0, 0);
mouse_event(MOUSEEVENTF_ABSOLUTE or MOUSEEVENTF_LEFTUP,
MousePos.x, MousePos.y, 0, 0);
end;