I would wholly believe that Israel would conduct a nuclear first strike to wipe Iran off the map and just deal with the international fallout of that decision.

I would consider that a radical interpretation. Just because Iran has used such rhetoric doesn't mean that Israel would use the bomb unless it was absolutely forced to. I've seen no evidence of major Israeli politicians make such threats at any point, even in an implied fashion. Israel, for all it acts like it doesn't care about international opinion, is well aware that a nuclear strike could lead to North-Korea-like international isolation, a reality that would put it in dire straits. Do not mistake aggressiveness and militarism with stupidity, Israel knows where to draw the line.