I
thought I might regret throwing out Job's words, "I repent in dust in ashes." I do. The analogy is imperfect. To apply it to Frodo is to jump into a bush of thistles, I think.
Now I must take my pruning hook to the thistle bush.

(If I may make so bold)
I don't know if Frodo has anything to repent of. Actually, I'm not sure the question is appopriate to ask. Why not? Because so far it's based on an analogy to Job, which I don't find altogether appropriate either, and I'm the one who broached it! Job's repentance in dust and ashes was, I think, if one looks at the context of the book, was because he thought he could do a better job of running the world than his God; which is precisely where Yahweh questions him. This was not at all what Frodo was about. So in that sense, the analogy was poor, and I rescind it (in dust and ashes). :P
Whether Frodo has anything to repent of or not, I must oppose, as kindly as I may, the general direction in
Fordim Hedgethistle's post (no wonder I came up with the thistle analogy!). It splits hairs. Such hair splitting is called "casuistry", which developed, at least among Protestants, as a new legalism after the Protestant Reformation. It had to be reformed from. Long story.
I don't think it works to use casuistry at all, and not in the context of Frodo's choice at Mount Doom. Whether stated negatively or positively, a choice was made by Frodo, whether or not his will was overwhelmed by the Ring. Does it make him guilty? The question doesn't matter to me, because I think it's beside the point.
Tolkien's purpose, in part, was to present an impossible task that a normal hobbit (read human being) would not be able to achieve, and would be broken by it. He succeeded admirably, to say the least. I think that he succeeded just as admirably in tapping into the reality of human existence in that
all of us, who truly live, have the impossible task of living whole lives. None of us succeed. Any of us who are willing to admit it, do, that we are broken, and need to be made whole. We need the numinous.
LMP