Being a non-resident, you can go to any police or sheriff department you want. Most will mail it to you in 60 days. The law allows for up to 60 days for non-resident. It does not require them to wait 60 days.
There is no difference in resident and non-resident permits, other than where you can apply. Residents are limited by where they reside.
Kitsap County Sheriff has a reputation for same day issuance. Go to their office in Silverdale.
Cost for resident or non-resident is $55.25. The fee is set by the state and cannot be changed by the local government.
You will need ID and cash/check. They will fingerprint you at the time of application.