Yeah. I always thought it was lame that you couldn't get scientific advancements from other civs through war. Guess they don't want to give war too much importance.
Depends on what are your aims for the war. At any rate, making war without significant technological advantage/numerical superiority/advantage in industrial capacity is neither easy nor fun. If that's the case, I'd say let them attack, repel their offensive and let them chill. The AI isn't that great at planning naval operations once you deal with the first waves. At that point, I'd aim for other victory conditions.
And unless you are thinking of turning the world into a wasteland in which the only remaining civ is yours, don't even think of using nukes. Don't bother building them, either. Everyone will instantly hate you when you drop the first, and most will declare war when you drop the second.
Ironically enough, it's perfectly fine to exterminate whole cultures with standard weaponry, but use a nuke and lo! world coalition on your doorstep.