Firearms were created for the purpose of combat. To exclude “military origin” rifles would be to exclude every rifle on this list.
I think that would be a stretch. AFAIK, the Remington pumps were never considered by any military, and there are a lot of rifles that were designed specifically for hunting, even though any hunting gun can be used for military purposes. I do not know if any military ever used the model 94 Winchester or the 336 Marlin. The Savage 99 was produced in a military model, but I do not think it was adopted by any military. Maybe a militia unit in the U.S. bought some. I only know of one drilling that was adopted for military use as a survival gun for the Luftwaffe during WWII.