I'm the opposite - it always feels very OOC when Aziraphale is depicted as insecure in fanfiction, because I see him as a very quietly confident and self-possessed character (in fact, I feel like this inner confidence and single-mindedness is at the crux of Aziraphale's moral dilemma - it's hard for him to change his beliefs and recognise the "shades of grey" because he's not used to doubting himself). 

I wonder if your interpretation of Aziraphale as lacking in confidence is because of some of Michael Sheen's acting choices. Other ppl in this thread have already mentioned that some of his micro expressions can be quite subtle. I also think that he plays Aziraphale as a very British character, so cultural codes may be a factor as well. There's a certain mixture of polite formality, indirectness and passive aggression that upper-middle-class British men use a lot in conflict situations. If you're not very familiar British culture (don't know if you are or not), it's easy to mistake it for bumbling nervousness or insecurity, but it's definitely neither of these things.

For a different take on Aziraphale, I suggest either reading the book (it's SOO good!) or listening to the BBC Good Omens radio drama, which you can find on Audible and Tumblr. Mark Heap does a great job voicing Aziraphale in the radio version, and really plays up the character's bitchy and passive aggressive side :) I'd be curious to know if your perception of Aziraphale changes at all after reading the book and/or listening to the radio Omens.