Actually the Nano is only 30 pins, but I don't think they make a 30 pin 0.6" wide socket. There may may a 32 pin.
If you go the route of using an IC socket, then the 0.1" square pin headers will not work. You will need to find machine pin headers that look like the round pin IC sockets. They are pricier than the square pin headers. I found and used them to mount a few Pro Mini's a while back.