Conny,
I won't comment on this particular navy because the pictures are so crummy. But I doubt seriously that any commercial navy Luger would have military/naval proof marks (crown M) on it. I went through my books regarding 1908 navies and my "Imperial Lugers" 1st edition book by Jan Stills did not mention a commercial 1908 navy. "Lugers at Random" by Charles Kenyon does mention it on page 118-9.
My book "The Luger Book" by John Walter does the best job of talking about the variation 1908 commercial navy on page 211. Mr. Walter has this to say about it:
"Navy Pistolen 1904 are invariably identified by their navy crown/crown M/crownM proofmarks and military cyclical-serial numbers, but 'navy commercial' could also be obtained. Most of these are 9mm New Model Parabellums with grip safeties, crown/crown U proofmarks on the receiver-side and crown B/crown U/ crown G marks on the barrels. Their numbers include 255064, 35682-38412, 43916, 51310-51357, 54099, 62151, 64302-64400 and 67943 (with gaps in the sequences), plus an additional handful of short-frame navy commercials in the 56747-58634 group without grip safeties. Though all survivors chamber the 9mm Parabellum, 58539 was sold by Stoeger in 7.65mm prior to 1917. In addition to the prewar examples that can justifiably claim to be genuine navy commercial Parabelliums, some post-1920 guns were made from cannibalized parts."
Unfortunately, Mr. Walter did not differientiate between the 1904, 1906, 1908 or model 1914 variations in this or any of the other books that he published on the subject. But he did mention navies without grip safeties which, I presume, would encompass the 1908 and Model 1914's. On a personal basis, I regard the 1908 version commercial navies in the 51000 serial range as legit. I have seen commercial navy Lugers with both the long and the short frame variation in that serial range. This was a transitional period on frames and maybe the factory just used up some spare parts that they had on hand. Much like they did on the 1917 artillery Luger front and rear sight adjustment pins in that transitional period.
Also, unfortunately, I put in a long day yesterday and today looks like it going to be another. I am sure that more has been written on commercial navies, but I am too tired to do the necessary digging. I hope that this helps.
Big Norm