No registration required in Washington state.
The key words in the law that you cited are "in a manner that warrants alarm". In State vs Casad the court ruled that the mere fact of openly carrying a firearm clearly did not warrant alarm in the average person. I believe there have also been cases where the court ruled that if the state had wanted to ban open carry they could simply have written the law to do so. The fact that they used the words "warrant alarm" indicates that they did not intend to ban all open carry.
I would reccomend the pamphlet that a member put together which many of us carry all the time but because we can't get stickies on this site I can't find the original link. Maybe someone can help out here.