Define "race cat." Is that one of those test pipes that's sort of shaped like a cat, but with no actual catalyst inside?

Luckily since the car is pre-'96 you don't have to worry about them scanning the OBDII diagnostic port.

Not sure if they have a visual inspection in Washington state, but as long as they don't then you just need to worry about making the tailpipe reasonably clean.

Mainly as long as the fuel is tuned properly and you have a real cat on the car, you should do fine with a sniffer test.