We went out with the Messenger of Allah ﷺ pronouncing Talbiya having no explicit intention of Pilgrimage or 'Umra. The rest of the hadith is the same.
خَرَجْنَا مَعَ رَسُولِ اللَّهِ ﷺ نُلَبِّي لاَ نَذْكُرُ حَجًّا وَلاَ عُمْرَةً وَسَاقَ الْحَدِيثَ بِمَعْنَى حَدِيثِ مَنْصُورٍ