This is simply a larger-scope version of the question "If you could travel through time/If you had foreknowledge of the significant events, would you kill Hitler (or other applicable human rights violator) before he rose to power?"
Also, it's related to the following moral dilemma:
"You are standing next to a railroad switch. There are 5 people stranded on bridge A and 1 person stranded on bridge B. Do you switch the train from A to B track, saving the 5 people but dooming the 1 person?" Do you preserve your own culture or preserve the culture of the enemy? It sort of depends; if this is a matter of the enemy being completely aggressive and your country being utterly on the defense, I'd say it's a justified reaction. A country that just aggressively attacks is, on average, going to be less value to the progress of mankind. On the other hand, if YOUR country was the aggressor and found out the other country weren't the weaklings you thought they were... you probably lack morals and ethics anyway and wouldn't think twice about it.
Given the assumption that if you don't use this weapon, your own culture will be, essentially, wiped out; your inaction will likewise cause a culture to be wiped out. So if a culture will be wiped out either way, self-preservation dictates you'd try to preserve your own culture since that would ensure your survival. Note that this is assuming an all-or-nothing scenario. Ideally, there would be peace talks, diplomacy, etc.