There is a separate front panel header that you can connect a remote power switch to. It is item C in the diagram shown on page 15 of the NUC's Technical Product Specification (TPS). Here is the pinout for this header:
Yellow Pins 1, 3 SSD/HDD Access LED.
Green Pins 2, 4 Power LED
Purple Pins 5, 7 Reset switch
Red Pins 6, 8 Power switch
Bottom line, you want to connect a normally-open momentary contact switch to pins 6 and 8 of this connector...