Your example is politically loaded. Let's try a simpler one.
Joe makes a vow not to eat chocolate. Then he finds himself on a desert island where there is no food other than chocolate, and he will otherwise die of starvation. (Or more simply -- he's having a diabetic emergency and the only available food is chocolate.)
The prohibition of violating a vow is "he shall not violate his word"; the theoretical punishment for doing so is lashes.
The categorical rule of Jewish law is that the only commandments that can't be broken to save a life are murder, idolatry, and a handful of severe sexual offenses. (All of which theoretically carry the death penalty.) I've heard lots of discussions of other exceptions (e.g. what should a judge do if he fears for his life), but never anything about oaths. Therefore saving a life would override an oath. (Furthermore, we believe an oath could be annulled; it would be easy, time permitting, to assemble a rabbinic panel and retroactively regret not having inserted a life-or-death clause into the original oath.)
Questions of to what degree soldiers are expected to follow orders without question, for the broader good of the nation, arise independently of any "oath" -- you're welcome to ask that as a separate question.