Yes! There's a lot of ways to remove the original observer from the question.

The example I thought of (but ended up not including): If all one's credence were on simula(ta)ble (possibly to arbitrary precision/accuracy even if perfect simulation were not quite possible) models and one could specify a prior over initial conditions at the start of the Cold War, then one could simulate each set of initial conditions forward then run an analysis over the sets of initial conditions to see if any actionable causal factors showed up leading to the presence or absence of a nuclear exchange.

A problem with this is that whether one would expect such a set of simulations to show a nuclear exchange to be the usual outcome or not is pretty much the same as one's prior for a nuclear exchange in the non-simulated Cold War, by conservation of expected evidence. But maybe it suffices to at least show that the selection effect is irrelevant to the causal factors we're interested in. Certainly it gives a way to ask such questions that has a better chance of circumventing anthropic explanations in which one might not be interested.