It is not stainless steel. It is simply polished steel in the white. I would try any of the links to stock makers we have here on Graybeard and would also go to Boyds Stocks for a stock for a small ring Mauser.
The M93 and M95 Mausers originally chambered in 7x57mm are perfectly safe for the 6.5x57mm cartridge - they are all within the same pressure tolerances these actions were built for. The M96 action begins the Swedish line of Mausers which ended with the short version (23.5" bbl and turned down bolt handle) M38 and you can find M96/38s in 7x57 and 8x57 Mauser as well.
Dale - I would rescope that baby and restock it. It looks to wear a mil-spec barrel, so Sellier and Bellot 131 gn soft nose should give you better than acceptable accuracy and it is a serious game getter. Do not bother with any US made 6.5 Swedish ammo, go for the euro made, it is much better. Good Luck.