I've had to pour bottles back into the priming bucket before because I forgot priming sugar, never really noticed excess oxidation, so it should be less bad to pour it carefully into the keg since you are just going to close it up right away, not expose it to more air to re-bottle like I did. Just purge the air space in the keg with co2 before closing it. Or with or without doing that, put a little yeast (maybe something designed for higher gravity like champagne yeast?) in some bottles and wait to see how those do. I'd think for the small size of the bottle opening, you are exposing it to pretty little oxidation and adding the yeast to the bottle shouldn't really hurt much. You could keg it all, keg some and yeast some, or just yeast a few, or yeast all, even leave some bottles alone if you are worried about risking it.
Above all, if it tastes decent, it should get drank, right?