The most effect strategy depends on the circumstances. If Snowden can maximize publicity by playing cat-and-mouse with the U.S. government for weeks, maybe that's a good enough reason for him to resist being arrested by U.S. authorities. The implications of personal conscience also depends on the small print. People might agree with your general argument for the draft, but at the same time deny that the Communist takeover of Vietnam was anything close to a national emergency. After all, the eventual defeat in Vietnam did not cause the U.S. to cease to exist.
Many contemporary political philosophers seem to take Gandhi and MLK as examples, but I'll take Hobbes and Locke any day over them: as soon as the state steps over the limits of its strictly circumscribed powers, you are under absolutely no obligation to obey the parts of its law that exceed the limit. You may voluntarily choose to obey the punishment part for one reason or another, but that's just your choice and it's irrelevant to the legitimacy of your cause. (Hobbes said that death row inmates have the right to try to escape from prison, because in his theory, the state was never authorized to execute people.)