Since I have no components, its a little hard to start with a schematic.
Connect with VIAs? I think you MAY have your terminology wrong, A VIA is a very small plated hole connecting one side of a PCB the other. You need pads for connecting a PCB to a PCB.
What you do is add terminals to the schematic and connect them in an interconnecting schematic.
You are kind of thinking of component wrong. Find a component that give you a hole pattern on the PCB that you want and add it to you Schematic, just because you are not going to mount on the board does not mean that you can not use it to lay out the PCB for what you need in holes spacing. You can then wire any of those component on the schematic for any traces you want.You can make components for your needs like one for a rework area.
You should seriously mull over making a pattern in your PCB board plan, somewhat littler than the impression of a little Arduino board (like the NANO), with cushions that coordinate all around the edge of your pattern. It should then be quite simple to fix up the Arduino board with the cushions, either on the best layer or patch side, and cautiously bind the two together from the edge. That will totally dodge the additional room taken up by even the shallowest header connector. Furthermore, the PCB pattern likely won't include anything (or at most pennies) to the expense of the board creation. As I've been enjoyably shocked at the Truly sensible costs from a portion of the China based PCB manufacture (PCBWAY.COm for instance), and these fab houses can include such patterns easilly and inexpensively.