I haven't been on this tour, but a quick search on the web showed the following . . .
Mena House - Cairohttp://www.menahousehotel.com
"24 hour laundry service"
"lower Sun deck with . . . . laundry"
Steigenberger Nile Palace - Luxorhttp://www.steigenberger.com/en/Luxor
"Laundry and dry-cleaning service"