In answer to your specific questions:
Are there known dream scenes where he has no wedding ring?
No. In every dream sequence (with a single exception where his hands are in his pockets throughout the short scene) Cobb is always depicted as wearing his wedding ring, including those set in flashbacks prior to Mal's death.
Are there known real world scenes where he's wearing his wedding ring?
Yes. In the flashback scenes leading up to Mal's suicide and the scenes depicting Cobb and Mal's 'dream experimentation' Cobb is seen wearing his wedding ring. In all of the present-day scenes set in reality, he's always depicted as not wearing his ring.
In conclusion, given that he's seen wearing his ring in both reality and dreams, it would seem to be useless as a totem. That being said, the concept of even needing a totem (to determine reality) appears to have been something that came after Cobb and Mal got stuck in Limbo.
Based on Cobb's speech to Ariadne, it looks like Cobb and Mal were among the first people who'd ever spent long enough in a dream-within-a-dream to actually need a totem, and even only then after the dangers of confusing reality with dreams became frighteningly apparent.
COBB: We were on a job. Exploring dreams within dreams. But we didn’t understand how your mind can turn hours into years. How you can get trapped. Trapped so deep that when you wash up on the shore of your subconscious…