Bring a tote bag, or some sort of small, light bag you can easily and comfortably carry at all times. You can keep your shoes in it when you go to the masjid, to keep them with you. Carry a few of your essentials with you this way, sometimes it can be a while before you can get back to your room. Maybe pack a light snack, a journal, a pocket Qur’an, etc. When you pray, just keep it on the ground in front of you. When you make tawaf, wear it on your chest instead of your back. Pretty easy.
You won’t have to worry about passports. The Hajj Ministry collects those when you arrive in the country (yes, that’s right). They return them to you, miraculously, before you leave to return home. For your cash, it’d be safer to carry it on you, you can get like a money belt to wear around your waist. I used to also keep essential Hajj guide printouts and du’a lists, along with my Hajj IDs in there, so it can be really handy.