The Outdoorsman came along in 1931, starting with #36500. It had a "one screw" adjustable rear sight--the one screw being for elevation adjustment. Windage adjustment was accomplished with two screws, one on each side.
S&W target sights would "shoot loose" (as respects elevation adjustment) right from the get go---S&W's theory being either the barrel catch cam spring (on top breaks) or the sight tang (on hand ejectors) would provide sufficient resistance to prevent such irksome happenings.(They were close to correct with the top breaks, and not even close with the hand ejectors.) I suspect the coming of the Outdoorman provided an awakening, and the "two screw" rear sight was not long in arriving (1932)----and no way in hell was ANYTHING with that sight going to "shoot loose"---when it was properly adjusted and locked. As an aside, misunderstanding runs amuck to this day when it comes to the proper adjustment and locking of the "two screw" sight. (BOTH screws are employed with elevation adjustment AND locking-----BOTH SCREWS!!)
So question #1 is which sight is on your gun---the one with one screw for elevation at the hind end-----or the one with two screws at the hind end? Actually, that question is somewhat rhetorical because alternative sight blades were available from the aftermarket. (I had a white outline rear sight blade (from King) on a third model single shot from 1923.) If yours is from KING, it will be so marked. Removing it to have a look is simply a matter of loosening the windage screws (more than a little bit), and plucking it out.
The Patridge front is correct. The red bead gives me pause, because the beaded sights of the time were one (with the bead on the face of a Patridge)----the Call---and its beads were either gold or ivory ---so my knee-jerk reaction is either the sight's been messed with-----or replaced. (Replacing a front sight blade is child's play.)
Ralph Tremaine