Hi,
There's a positive and a negative here for the Bible and Xian theology:
I think the most straight-forward interpretation of Genesis 6 is that the sons of Adam and Eve married the daughters of other humans on the earth and that their children were giants among men - great leaders, "mighty men" and "men of reknown".
It would be difficult to harmonise other humans on earth that were not descendents of Adam and Eve with that of the Xian concept of sin. The Bible specifically states that Adam and Eve's offspring were cursed, so if there was another unrelated group I don't see how they would inherit sin.
On a positive note, if the term Nephilim referred to 'mighty men' or 'men of reknown', it would remove the contradiction of there being Nephilim before and after the Flood, since we have mighty men in every era of history.
I do think you would struggle to make the term stick to your interpretation given the various descriptions in the bible, even gen. 6:4 may undermine your theory since it mentions 'giants' and 'mighty men' in the same verse.
Regarding this:
product of a union between angels and humans.
A strict reading of Genesis 6:4 doesn't actually say that the Nephilim were involved with the women, the verse only testifies to the presence of Nephilim before and after these marriages happened.
From the KJV:
There were giants in the earth in those days; and also after that, when the sons of God came in unto the daughters of men, and they bare children to them, the same became mighty men which were of old, men of renown.
Nephilim is translated as 'giants' here. But, if you actually read the passage it is clear that it was sons of God who came to the daughters of men, and not necessarily the Nephilim.
Sons of God is a difficult term to deal with fully, but in the Hebrew Bible it can be used in the context of 'having the nature of' or 'showing obedience to', it can also refer to the nation of Israel of Ephraim (Exodus 4:22, Deut 1:31 and Hos. 11:1)
Nephilim can also be translated as 'the fallen ones'.
Brian.