Certainly in the UK, 'or' and 'awe' or very similar. But I'm pretty sure the same is true across the states. The 'awe' in 'awe, shucks' is not even really a word, just a sympathetic utterance in the same sort of class as 'um' and 'aaah', so I don't think it has an official spelling, just a phonetic approximation. It is certainly distinct from the word 'awe' that's the root of 'awesome'.

Edit: I meant to point out that I have never seen 'awe, shucks' written before, always 'ah' or 'aww', but I can see how it might be written that way based on a Midwestern accent.

US pronunciation is generally rhotic, ie. they will pronounce the r's distinctly in those words. Most of the UK (the southwest being the largest exception) is non-rhotic, as are Australia and New Zealand, and in those accents those words generally would be indistinguishable.