Keith
As Garfield stated above “ In all probability, your pistol was reworked during the Weimar period, and routed to the Reichsmarine where it remained in service after the Nazis took control. “
The N.1804 property mark signifies Marinestation der Nordsee (North Sea) headquartered in Wilhelmshaven. As TomA stated "It was property number 1804." During the Imperial Era, Navy Lugers issued from this site were stamped W.W..xx . The W.W. signified Werf zu Wilhelmshaven (Dockyard at Wilhelmshaven). Lugers issued from this Marinestation or Dockyard were issued to a variety of German Navy ships and personnel during the Imperial/Weimar/Nazi era.
In my opinion, your N 1804 stamp was applied during the Nazi Era. Tables listing property stamps and Luger Models are on page 204 of Weimar Lugers and page 145 of Axis Pistols. These indicate that your property marking, N1804, was applied sometime during 1935 -1937.
N1785, N1819, and N1866 are also reworked 1906 or 1908 Navies. N1785 is shown on page 223 of Weimar Lugers and has its barrel chopped to 4 inches, the front sight reattached, and its grip safety removed. It retains its Imperial Navy proofs and like yours does not bear the Navy Eagle. These Imperial reworks usually do not bear the Navy eagle. Your reworked 1906 Navy fits in very well with this group of other reworked Imperial Navies.
Photographs showing you Luger would be of interest.
Jan