I would place an access point at the top of the shaft, with a high gain directional antenna pointing down, then try a wireless enabled device (laptop, PDA, etc) in the elevator cab to see what kind of connectivity you can expect. If you cannot get a reliable connection inside the cab at all floor levels, (due to sheilding from the cab structure), you can install a WLAN repeater (range extender) in the cab, placing the donor antenna on the roof of the cab pointing up.
I would try a temporary access point in the shaft first to see what kind of penatration you get.
If you get good signal penetration with the cab about halfway up the shaft, but cannot cover the lower floors, you could place access points at the top and bottom of the shaft, and the user would roam between the two.
A patch antenna is basically a flat antenna about 4" square, that would attach to an acccess point/repeater in the cab. The "stub" antenna I was referring to is a small, unity gain or 3dB gain omnidirectional antenna that can be permanantly mounted to the cab's exterior/roof.