+1 to that!
In our beloved state there is no hassle, it's done the constitutionally RIGHT way!
You'll be going to whatever main court building is in Seattle--in Tacoma it's the county-city building downtown.
Welcome to the club (when you get that permit, that is). I don't know what your level of training is, but be sure you're knowledgeable, safe, and well trained before you decide to carry--for your sake as well as the rest of us that exercise our 2nd Ammendment rights (if you already know all of this, disregard!).