How to add an RC filter between a header pin and a ribbon cable
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 k&Omega; as a pullup.

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