It's not wise for small nations to give big nations the bird like that when there are other options. GP's suggestion is much more tactful because nobody worth taking seriously is going to argue with the idea of selling property to the highest bidder whereas dumping stuff in the ocean is generally frowned upon by everyone.
Declaring war on the United States with a threat of intentional nuclear warfare against its population would be a particularly bad idea. That'll get your sovereignty revoked very quickly via military occupation.
The response to what I said of course is: yeah but the US is doing a bad thing. That's correct and it changes absolutely nothing about the fact that declaring nuclear war on the US, declaring the intention to try to harm its people with nuclear material, is a bad idea. Fairness is never going to exist between a superpower and weaker nations, it never has, it never will. The superpower dictates the terms in nearly all cases.
Isn't there an old film where a small island declares independence from the US, declares war on the US and then surrenders after 5 minutes to get aid?
(Edited because I think it's actually colony's not colonies)
I feel like it was an episode/arc in The West Wing.
Of course this should never be done, as it is some sort of eco-terrorism, but is one of the many ways the US can have their hands forced.
Edit: in case this is not clear, I am never advocating for something like this to happen. But it is always a stupid idea to leave potentially lethal and dangerous materials on the land of a place you've scarred and destroyed and which doesn't want it at all.