Inoculating a nation’s population against a biological weapon [...] If done in public, it is likely to provoke a conflict.
You could use the pre-existing differences between your population and the targets. In nation states, you could make the virus decide by presence of absense of certain DNA markers. Or you could make the virus lethal/harmless for people who drink milk / eat pork / consume lots of corn syrup...
It will not be perfect, but in a war, certain losses are often considered acceptable.
Of these ideas, genetic markers seem like the best way to go. They’re discrete and hard for a target nation to emulate. You don’t even need 100% coverage to keep your population (mostly) safe. The most important thing is to keep R0<1 in your nation and R0>1 for the enemy.