You might consider making a cutout in your PCB board design, slightly smaller than the footprint of a small Arduino board (like the NANO), with pads that match up all around the edge of your cutout. It should then be pretty easy to line up the Arduino board with the pads, either on the top layer or solder side, and carefully solder the two together from the edge. That will completely avoid the extra space taken up by even the shallowest header connector. And, the PCB cutout likely won't add anything (or at most pennies) to the cost of the board fabrication. As I've been pleasantly surprised at the VERY reasonable prices from some of the China based PCB fabrication (PCBWAY.COm for example), and these fab houses can add such cutouts very easilly and cheaply.