I am thinking you are very right on the cost piece, hand claws make the most sense. The arm is a wicked idea, I am thinking however that the cost is going to be pretty overwhelming.
the only thing that I am really confused on is the fact he is wanting them to be needle like and used as injectors.
Try this:
Full Obvious Cyber-Arm (Alpha-ware) [This means all additions will be Alpha as well]
Bulk Modification- Rating 4
Customized Agility
Customized Body
Customized Strength
Enhanced Body- Rating 4
Enhanced Agility- Rating 4
Enhanced Strength- Rating 4
Armor- Rating 2
4 x Fingertip Compartment
Retractable Climbing Claws
The "climbing claws" could be stylized more as "syringe needles" instead I would imagine (just remove the actual climbing bonus). If you want that modification on the claws to cost still more, then you could charge double the Alpha-ware cost for the claws.