Hi Bill,
I am a KM collector and not so much a weapon collector but based on what you have shared with me I can tell you this about your HSc.
Based on the serial number it falls into the production of what is called the forth variation from 790000 to 886000. Over the course of production several changes were made to either improve the weapon or, more frequently, to make it cheaper and easier to produce. Examples of changes were position of grip screws, material of grips and finish, quality of final machining and blueing, etc. These had an eagle over 135 acceptance stamp. 135 was the waffenamt number for Mauser Werke AG, Oberndorf am Neckar, Germany. The eagle over N are the firing proofs. These did not have the final machining to the mirror finish and the blueing was not the deep blue/black but now had a grayish, cloudy tint. Prior to this there was a cross hatch strip on top of the slide in the site channel but with this type that was no longer done. Based on the lists I have the serial number on your piece does not match KM contract numbers. So this is most likely a Heer issue piece. Having said that, the navy was known to accept weapons made on Heer or Luftwaffe contracts to quickly fullfill their needs and there have been weapons obtained directly from vets who took them off of KM personnel or stores that are devoid of KM markings and not in KM contract serial number ranges.
Regards,
Mike