Am I risking a short circuit/gaping situation?
The breakdown voltage of air is about 3kV/mm, so there will be no problem. With 5V this will be 1.7µm.

And if you leave always 2 rows of copper squares alone, there shouldn't be a problem with short circuits.

But:
If you want to use about 100 LEDs (each drawing 20mA i assume?) each of the 7805 (you use 3 all in all?) will need about 700mA.
I don't know your input voltage. But depending on it and Ohm's Law the 7805 will be pretty hot...
You can calculate the power dissipation with
$$
P_W = (U_{in} - U_{out}) \cdot I_{out}
$$

In your datasheet you will find a diagramm showing IC temperature over P_W.