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.
What part of the UK? They are wildly different in Scotland, Northern England, Northern Ireland, in fact probably anywhere except for the south of England, and even there it doubtless varies.
Really? Can you have a stab at describing the difference? Because I've spend the vast majority of my life between Edinburgh, Nottingham and Leeds and I can't bring it to mind. I can see a slight differentiation in places with more solid 'r's (Scotland and the borders for instance), but any wild variation escapes me...
That's the difference though isn't it? Come to glasgow and hear the intensely rhotic pronunciation of "or" and compare to "awe" which has no R at all. The two words sound very different.
"burger" in much of the UK is completely rhotic, with both R's intensely rolled, while in other parts it is more like buhguh. Really sounds quite distinct to my ears.
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.