Paying what you owe isn't morally wrong. But using your wealth to corrupt the system so that you and you ilk owe less in taxes IS morally wrong. Its also wrong to support,continue and benefit from the system that keeps the corruption in place.
To avoid ("legally" or fraudulently) taxes is to push the burden onto the people who are paying their appropriate amount of taxes.
But to contribute to a corrupt, warmongering government, is also wrong.
What you can do - what I do - is choose to live in a higher taxed country that isn't nearly as bad with respect to how it spends tax money. And so long as you pay more taxes to the country you live in, you end up owing none to the US.
Since you aren't in the U.S., though, I guess there isn't much you in particular can do.
US military is not particularly known for its altruism. You may want to rethink the internal logic of your argument here.