They appear to be Weaver HIGH rings. You appear to have about a half inch clearance at the hammer.
Like Andy mentioned, how does the rifle fit you? If you close your eyes, and shoulder the gun, then open your eyes, what do you see? I'm suspecting you will see the hammer and the bottom of the ocular on the scope.
I'm certain that medium Weavers will work, likely even lo's. I prefer steel rings to the allow weavers. Burris ZEE rings are a favorite here, I prefer the Leupold PRW or WARNE maxis rings. I would think either will work in lo height.
Yes your hammer spur will still work and likely be even more necessary.
CW