Yeah, put the zener after the switch. Use something like the microschematic at
wikipedia. (i.e. band to switched 5V, other side to ground) If you get it backwards you're destroy the zener diode, and if you put the zener in series with the NES instead it won't work at all, so the failure modes aren't that awful.
It doesn't look like removing the RF/A/V/power regulation module should affect the reset button, that's shown on the "third" page ("NES 3") in the lower right corner. Note that that's the only place I've noticed the schematic is in error: it's drawn as
5:wire 4:LED 3:switch and it should be
5:LED 4:switch 3:wireedit: fix braino