You can bypass the router functionality (e.g. NAT) by not using the WAN port on the AP/router. I.E. connect into one of the LAN switch ports. Elementary stuff, and exactly as GG specified in post#2.
SD
Dependent upon router. There ARE (cheap & nasty) routers out there which will attempt to introduce NAT into the equation irrespective of whether it's connected to a LAN port.
/voe.