Actually, I recommend the Client Bridge mode and not Client mode, if I may use the names that are used in dd-wrt.
If you go the dd-wrt route, you'll see several options under Wireless Mode, including "Client Bridge" and "Client". The difference between them is that Client Bridge simply extends your existing LAN, (I think this is what you want), while Client mode creates a new subnet for the devices hanging off its LAN ports. So in Client mode the result would be a double NAT situation, which is generally less desirable unless you have unique requirements.
In both Client and Client Bridge modes, no wireless devices can connect to this router since its sole purpose is to connect to an access point, which will be your wireless router downstairs. Therefore, the laptop would only be able to connect (wirelessly) to the router downstairs, or via Ethernet cable to the flashed router upstairs.