I do think he has a sort of brasveness - I think he needs to to live his life, and he did a lot for the order (such as looking into werewolf packs etc which is pretty hardcore). In fact, I think he has a lot of the gryffindor hard-headedness and recklessness, he's just usually quieter than some about it.

I haven't thought about Lupin in a while, it's interesting to consider him with closed canon.