You don't have to construct the model at that level of detail to meaningfully discuss the issue. Just look at the base rate of presidential assassinations and update that to cover the large differences with the Kennedy case. If you're trying to simulate a universe without Lee Harvey Oswald, you're probably overfitting, particularly if you're a human. Your internal model of how Kennedy was actually shot doesn't contain a high-fidelity of the world in which Oswald grew up and went through a series of mental states that culminated with him shooting Kennedy (or at least, you're not simulating each mental state to come to the outcome). Instead, you have a model of the world in which Lee Harvey Oswald shoots JFK, and otherwise doesn't really factor into your model. While removing Oswald from the real world would have large effects, removing him from your model doesn't.

I think that you ask "what are the chances that Kennedy would have been shot if Oswald hadn't done it?" you're probably asking something along the lines of "If I build the best model I can of the world surrounding that event, and remove Oswald, does the model show Kennedy getting shot, and if so, with what confidence?" So in order to settle the wager, you would have to construct a model of the world that both of you agreed made good enough predictions (probably by giving it information about the state of society at various times and seeing how often it predicts a presidential assassination) and seeing what the answer it spits out is. There might be a problem of insufficient data, but it seems pretty clear to me that when we talk about counterfactuals, we're talking about models of the world that we alter, not actual, existing worlds. If many worlds was false and there was only one, fully deterministic universe (that contained humans), we would still talk about counterfactuals. Unless I'm missing something obvious.