وَلَا بَأْسَ أَنْ يَغْتَسِلَ، وَيَدْخُلَ الْحَمَّامَ، وَيَسْتَظِلَّ بِالْبَيْتِ وَالْمَحْمِلِ.
Translation: There is no objection to the pilgrim bathing, entering a bathhouse, and taking shade from a building or a covered litter.
Iḥrām does not ban cleanliness or ordinary bathing. Al-ḥammām refers to a bathhouse, and al-maḥmal a sheltered litter historically carried on a riding animal.
Permission to bathe does not in itself license hair removal, perfume application or other prohibited acts. Those conditions remain relevant.