Bogachiel State Park should have showers, though they may be currently closed for the winter. Their phone number is on their website, you should be able to give them a call for more information: https://www.parks.wa.gov/478/Bogachiel
Not sure what your situation looks like but people in my city will pay for a gym membership and use those showers daily. Ours is $35 a month which might be too pricey but it would be a solid investment for hygiene
Salt Creek has coin showers. If you go to Sol Duc Hot springs they have a locker with showers as well. We did the hike then showered and soaked in the hot springs for an hour
etcpt t1_je322ub wrote
Bogachiel State Park should have showers, though they may be currently closed for the winter. Their phone number is on their website, you should be able to give them a call for more information: https://www.parks.wa.gov/478/Bogachiel