Dear Hayley,
You can contact Nadine Chahine (she's also a member of Khatt) who has designed several fonts specifically for signage.
Big Vesta Arabic (you can see samples of it in the Khatt Project Typographic Matchmaking V1.0) also a Frutiger Arabic font that had its debut in the signage design for the American University of Beirut.
She can give you additional information as Arabic Fonts expert at Linotype.com
Another reputed type designer (and khatt member) to contact is Pascal Zoghbi.
All the best with your project