Manually triggering a low active pin

Putting a resistor in line as you describe is one way of dealing with the noise problem, but it also requires hacking up the board. I'd try simpler solutions first that only require adding components, not breaking things. You can always break a trace later if the simpler solutions don't work, but I think there is a good chance they will do just fine.

You don't say what microcontroller, but from the description it seems it has a typcial reset input with negative logic. Hold it low, and the micro stays in reset. Hold it high and the micro is allowed to run. Actually I'd rather call that a RUN input so that the name corresponds to positive logic, but that's just silly me trying to avoid confusion.

In any case, whatever micro this is is apparently OK with 1 nF on this line. Go ahead and put that there. That alone might be enough to solve the problem. The noise is probably capacitively coupled so is coming in with only a few 10s of pF at most in series. 1 nF should swamp that. I would also add a pullup to Vdd. That makes it so the noise has to provide more current to drag the line low, something it will have a hard time doing with the aformentioned capacitance in series. Again we don't know the micro or any of its particulars, or probably more importantly the particulars of the programming jig, so I'd stick with 10 kΩ as a pullup.

So to summarize: Slap 1 nF to ground on the RUN line and 10 kΩ to Vdd and leave the surgury for mad scientist stuff you'll be adding later. Most likely that will fix things well enough.

Using an external watchdog circuit to cycle the power to all your on-board circuity is a rather good idea. It helps to cover cases where some stray external event has caused an upset on some silicon chip circuit. Sometimes these events, whether they be high voltage spikes, reverse bias on signal inputs or even alpha particles can cause localized latchup on-board the chip and the only realistic way to clear such fault is to cycle the power.

Using the scheme to connect the WDT to the enable of the voltage regulator does require some due diligence on your part.

a) Make sure the WDT circuit is not powered by the same voltage rails as the disabled regulator.

b) Make sure that the length of time that the regulator is disabled is long enough. Bypass and filter capacitors on the output of the regulator need to discharge to the greatest degree possible in order to qualify as a power cycle to the silicon. In many instances a millisecond or so of disable time will only allow a partial discharge of the output rails.