Don boycotts hurt the wrong people (i.e. the workers)?
Quite the contrary. If a boycott movement shifts consumer habits toward Fair Trade and other alternatives then workers (albeit different workers than those in the targeted country or company) are actually benefitting. Furthermore, workers in the targeted companies can take action as well and protest the fact that their labor is being used to hurt other workers in other countries through militarism. Even if a boycott were to hurt some workers over others, its damage could hardly be compared to the anti-working class devastation that is wrought by war.