I think the 10,75x52R spinger was created after 1904 because dont know it better till now. all top levers so your rifle is looking much older for my taste but we will see.
thats how doubles and singles have look in the 1914 catalog

1924 springer catalog

a single shot hammer rifle like shown into this catalog, was a 8mm caliber iirc

I got this drawing from Harald Wolf in belgium last year. 15 years ago he was making a lot of ammo for an older gentlman who was dieing before the order came to an end. this order was very official including CIP proof for the ammo in Liege.

9,3x53R Sako 10,75x52R Springer 10,75x57 10,75x68

custum loaded ammo from Samereier in Germany for a 10,75 Springer double rifle with the old components from Harald Wolf