Fascinating. Classic example of the provenance of gun ownership probably creating more value for the gun, than just a another well made neat old german made gun, with a sling. I will have to take your word for it that is a W that is engraved. I mean it could be interpreted as an "M" the way its broken, but no expert of German, text, alphabet or fonts.
Just guessing but it appears to maybe have been made early 1900's and maybe prior to WWI, but still that is a guess, but probably a strong obvious one. Do you know when that gun maker was active. I mean it could have been made in the 30's as well. If you know the time frame then that could limit your search to appropriate era. Again no expert on German history but not certain they were crowning or gifting too much to nobility after WWI.
Went to this site and then found these listings or people in that era. If its an M then maybe they could be for a woman Maria or an heir Maximin. Who the heck knows. If a W then it could be Weinsberg.
http://almanachdegotha.org/id101.html
h) Eleonore Johanna Marie (Seebenstein 24 Jun 1858-Móor 14 Feb 1938); m.Vienna 22 May 1883 Heinrich Gf von Lamberg (Preßburg 16 Jul 1841-Ottenstein 17 Oct 1929)
2h) JOHANN Nepomuk Adolf Maria Hubert Maximin Fst zu Schwarzenberg (Vienna 29 May 1860-Vienna 1 Oct 1938); m.Vienna 27 Aug 1889 Therese Gfn von und zu Trauttmansdorff-Weinsberg (Oberwaltersdorf 9 Feb 1870-Neunkirchen 12 Aug 1945)
Also it appears the reading the history of Schwarzenberg that alot of their holdings were in what is now Czech Republic. Now here is my wild ass theory that I have no basis but just throwing it out there. When the Nazis invaded Czech region they took possession of their holdings and the Schwarzenberg family is said to have fled not wanting any part of the Nazi party. Maybe that gun went with them or maybe was left behind and Germans kept it as a war prize. Pretty thin.