if you are then i hope you are a watchmaker. its not difficult if you know what your doing, or so my watchmaker tells me, but i wouldnt know where to start despite owning several 5xx calibres.
i dont have a clue where you would find the details you require. i suspect it would be better to replace the spring so you know its correct.
the erratic second hand isnt a problem and doesnt affect the timing so i'd be inclined to leave it until the watch needs a service.
hope that helps a bit
Graham