Don't worry about living in King County. According to this article from the Seattle Times (
http://209.157.64.201/focus/f-news/1718588/posts) there are over 48,000 concealed pistol licenses granted in King County WA and over 200,000 statewide. You're not alone.
Here is the WA FAQ for conealed pistols
http://www.dol.wa.gov/business/firearms/faconcealfaq.html
And here are the requirements to get the Concealed Pistol License:
http://www.dol.wa.gov/business/firearms/faconcealreq.html
Fortunately you live in what's called a "Shall Issue" state. This means if you meet the requirements set out in the link above, the state "shall" issue you a permit.
If you can pass a background check, scrounge up $55.25, and wait 30-60 days (or less), you can tote your KelTec around.
Of course the SU16 is not the best concealed carry gun, but according to the WA law even "carrying or placing a loaded pistol in a vehicle" is a violation of the law that will send you to jail. So I'd say getting the permit may be a good thing even if you don't plan on carrying. Even accidentaly placing a loaded SU16 in your car is a violation of the law. With the permit, no worries.
As a bonus, your permit would also be good in LA, OK, MI, NC, MS, UT, MIZZ, OH.
link to more info:
http://www.handgunlaw.us/ and click on your state.
(Unless WA restricts carrying pistol like the SU16, you would then be allowed to bring it along for the ride. Maybe someone can chime in on some local restrictions or nuances to the law.)
Once again, don't carry your KelTec on your person or in your car (unless its in a case) unless you have a license to do so. Breaking concealed weapons laws comes with huge punishments.