If you don’t mind the drive try Evergreen Mowers
http://evergreenmowers.com/
They are right off I-5, Ash and 164th.
Looks like another guy can sharpen as well:
Rob’s Repair & Sharpening
206-243-0863
12230 1st ave SW
These are from a quick internet search in ‘reel push mower sharpening’. If you call a good cutlery store, they should also have info on lawn mower blade sharpeners in the area.