Might be that the spring for the cylinder stop is a little heavier weight/strength than that of the typical clyinder stop spring, that could account for it being a little more loud than the typical sounds made by a revolver.
But what you are hearing is normal, the first "click" you hear should be it being released from it's engagement with the trigger and coming into contact with the cylinder. The second click will be the cylinder stop dropping into it's recess in the cylinder for proper alingment of the chamber with the barrel.
There isn't much you can do to reduce the sound of the "click" as it is a pretty consistent part of normal operation of these revolvers, rather it needs to be consistent because if it isn't it might point towards potential problems.
It's a sound that should be present both in a double action pull of the trigger as well as cocking the hammer back for a single action pull.
If you are making a shot in double action those sounds are going to come only a fraction of a second before the shot is fired and it will make little difference, especially if you are adept at firing your gun in double action which it is advisable to put effort towards.
If you are cocking for a single action pull, that may not be advisable as it may relate to your concerns about having your location identified before pulling the trigger. First steps should be identifying your target and depending on location in the country, possibly identifying yourself while issuing demands to stop. Otherwise some claims of laying in ambush or some other garbage might be levied upon you by the DA, hey I hate stupid hypotheticals as well but it isn't outside the realm of crazy possibilities.
Sorry if this was unsolicited opinion but I don't think that the double action pull of an S&W is a handicap or that using the gun in single action is preferable in a defensive shoot.