Summary: the problem with Pascal's Mugging arguments is that, intuitively, some probabilities are just too small to care about. There might be a principled reason for ignoring some probabilities, namely that they violate an implicit assumption behind expected utility theory. This suggests a possible approach for formally defining a "probability small enough to ignore", though there's still a bit of arbitrariness in it.
Yes, you need risk tolerance / risk preference as well, but once we have that, aren't we already outside of the VNM universe?
No, risk tolerance / risk preference can be modeled with VNM theory.