I think you're using the wrong search terms. Of course searching for something like "Nano sockets" will give you bad results. The correct term is female header:
The cheapest way to buy them is in the 40 pin strips. You can cut them to length with dykes. You lose one pin when you cut them because there's no way to cut between pins.
Note there are two different types of headers. The regular ones like you have on your Nano and the round ones. The round ones are nice but not compatible with the square pins. The round pin ones you can actually break to length and can even avoid losing a pin at the break if you're careful.