I think it highly likely that the bulk of the originals went down in front of the Maxims at Tannenberg and Bolimow and then were picked up and scrapped.
The Germans did issue quite a number of 1891 rifles to their Navy in order to free up 98s for the Front, but the little Carbines would have been too short, they chambered a non-standard cartridge and the Germans realised that the big day for Cavalry was in the past. Cavalry remained a reconnaissance force, as it should have, and the trend was to longer barrels anyway. It would have been easier to issue '98aZs than to try to find and issue ammo for specialty troops operating with the poor MN.
I'm afraid that the bulk of them went to the smelter in 1914, '15, '16 and '17 and that the few left in Russia likely would have been worn out in the following 6 years of fighting. Transcaucasian federated Republics (Georgia, Armenia, and Azerbaijan) were not forced into the Soviet Onion until 1923.
Like the man said: unobtainium, absolutely chemically pure. If you were to talk REALLY nicely to Mister Putin, he MIGHT be able to find one for you, but that's about it.