Pete, Living in WA state and having about 14 antique cars, I know the Washington State law well. If you are running a restored plate, collector car plate, or a horseless carriage plate, you only need to run the rear plate. If you are running modern day plates like the modern cars wear, then you need to show both plates, front and rear.
You didn't say if you're running a year of manufacture (YOM) plate. If you are, then as other WA residents have stated, you only have to run a rear plate. Another interesting item is that the YOM is not the license number registered to the vehicle but is registered as an "accessory" and the actual license number is shown on the registration as the license number even though you don't have the plate. Look on your registration under accessory. If you're running a modern plate I don't know if they will give you a "waiver".