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.
You mean pin headers like these: Gold-Plated-2-54mm-Male-Female-40-Pin-Single-Row-Straight-Round-Pin-Header
Those pins fit into round pin sockets fine and they work even better with breadboards since they don’t open up the wire clamps the way the square pins do.