The OP is not limited to only Sheriff offices....
RCW 9.41.070 Concealed pistol license—Application—Fee—Renewal.
(1)
The chief of police of a municipality or the sheriff of a county shall...
13) A person may apply for a concealed pistol license:
(a) To the municipality or to the county in which the applicant resides if the applicant resides in a municipality;
(b) To the county in which the applicant resides if the applicant resides in an unincorporated area; or
(c)
Anywhere in the state if the applicant is a nonresident.
Chief Ed Green in Oak Harbor is a great guy, but I don't know their policies on issuing CPLs. I renewed mine at the Stanwood Police Department and received it in the mail about 10 days later. Back in 2003 or so when I first applied to Island County sheriff office, they waited exactly 30 days, by policy, before allowing me to go back and pick it up - I would not apply there. The woman working the counter there at the time was a - well, insert bad word here - because first she erroneously told my wife at the time that she had to obtain a WA driver's license because she was "only a spouse" of the military and not active duty, then she was really snotty with me when I had the audacity to call them on day 29 and ask about the status of my CPL application.