That level of precomitting is only neccessary if you are unable to trust yourself to carry through with a self-imposed precommitment. If you are capable of this, you can decide now to act irrationally to certain future decisions in order to benefit to a greater degree than someone who can't. If the temptation to go back on your self-promise is too great in the failure case, then you would have lost in the win case - you are simply a fortunate loser who found out the flaw in his promise in the case where being flawed was beneficial. It doesn't change the fact that being capable of this decision would be a better strategy on average. Making yourself conditionally less rational can actually be a rational decision, and so the ability to do so can be a strength worth acquiring.
Ultimately the problem is the same as that of an ultimatum (eg. MAD). We want the other party to believe we will carry through even if it would be clearly irrational to do so at that point. As your opponent becomes better and better at predicting, you must become closer and closer to being someone who would make the irrational decision. When your opponent is sufficiently good (or you have insufficient knowledge as to how they are predicting), the only way to be sure is to be someone who would actually do it.
Okay, I agree that this level of precomitting is not necessary. But if the deal is really a one-time offer, then, when presented with the case of the coin already having come up tails, you can no longer ever benefit from being the sort of person who would precommit. Since you will never again be presented with a newcomb-like scenario, then you will have no benefit from being the precommiting type. Therefore you shouldn't give the $100.
If, on the other hand, you still expect that you can encounter some other Omega-like thing which will present you with such a scenario, doesn't this make the deal repeatable, which is not how the question was formulated?
Related to: Can Counterfactuals Be True?, Newcomb's Problem and Regret of Rationality.
Imagine that one day, Omega comes to you and says that it has just tossed a fair coin, and given that the coin came up tails, it decided to ask you to give it $100. Whatever you do in this situation, nothing else will happen differently in reality as a result. Naturally you don't want to give up your $100. But see, Omega tells you that if the coin came up heads instead of tails, it'd give you $10000, but only if you'd agree to give it $100 if the coin came up tails.
Omega can predict your decision in case it asked you to give it $100, even if that hasn't actually happened, it can compute the counterfactual truth. Omega is also known to be absolutely honest and trustworthy, no word-twisting, so the facts are really as it says, it really tossed a coin and really would've given you $10000.
From your current position, it seems absurd to give up your $100. Nothing good happens if you do that, the coin has already landed tails up, you'll never see the counterfactual $10000. But look at this situation from your point of view before Omega tossed the coin. There, you have two possible branches ahead of you, of equal probability. On one branch, you are asked to part with $100, and on the other branch, you are conditionally given $10000. If you decide to keep $100, the expected gain from this decision is $0: there is no exchange of money, you don't give Omega anything on the first branch, and as a result Omega doesn't give you anything on the second branch. If you decide to give $100 on the first branch, then Omega gives you $10000 on the second branch, so the expected gain from this decision is
-$100 * 0.5 + $10000 * 0.5 = $4950
So, this straightforward calculation tells that you ought to give up your $100. It looks like a good idea before the coin toss, but it starts to look like a bad idea after the coin came up tails. Had you known about the deal in advance, one possible course of action would be to set up a precommitment. You contract a third party, agreeing that you'll lose $1000 if you don't give $100 to Omega, in case it asks for that. In this case, you leave yourself no other choice.
But in this game, explicit precommitment is not an option: you didn't know about Omega's little game until the coin was already tossed and the outcome of the toss was given to you. The only thing that stands between Omega and your 100$ is your ritual of cognition. And so I ask you all: is the decision to give up $100 when you have no real benefit from it, only counterfactual benefit, an example of winning?
P.S. Let's assume that the coin is deterministic, that in the overwhelming measure of the MWI worlds it gives the same outcome. You don't care about a fraction that sees a different result, in all reality the result is that Omega won't even consider giving you $10000, it only asks for your $100. Also, the deal is unique, you won't see Omega ever again.