I often call myself an apatheist. Technically, I am an agnostic atheist, though the term is awfully broad. More specifically, I am an apatheist because I'll live my life this way whether there's a god or not.
Even if god were real, it doesn't show itself to us, so I cannot base my morality on its demands. It doesn't matters in my life whether there is a god or not. Should that hypothetical god be benevolent, then it would judge my actions fairly. Should that god not be benevolent, then I'd have no guarantees of it rewarding anybody based on their actions.
It's a fairly stress-free attitude since the notion of gods is so far beyond our comprehension that I can worry about more relevant matters. One of those is the concern of theists in government seeking to control how I live my life. I am very interested in that, but that's more of a terrestrial concern and not celestial.
I remember having a conversation with a girl when I was in High School about the existence of god, and she said, "But what if you're wrong!" And I said basically, "Oh well." That's similar to what you are talking about.