The diamond grips and flat latch make it early J, I suppose. During that improved I to J transition I would suppose it more likely than later times. Or a .32 misrepresented?
I'm keeping an eye out during the day on this one. Most interesting.
Got out the SCSW (2006) - here is a quote from p. 208
"A Model 36 with 6" barrel in blue finish with square butt has been observed in the 337XXX serial number range. Our current understanding is that this barrel length was not "officially" offered by the factory, but that some, perhaps around two dozen, may have been so altered before shipping. Accordingly, they may be difficult if not impossible to authenticate. Reported value in the $1500 range."
It would be very interesting to get the serial number and get a letter of authentication from S&W and (if possible) find out how it was equipped when it left the factory.
A 22 on that frame would be a six-shot. The flute is in the correct position for a 5-shooter. If it is a 22, the cylinder was staged to make it look like a 38.