No one can tell you today what the smoke and air quality will be like in a week. Have an alternate plan.
And now for the rest of the story.
199 is also a prohibited CA route for 40' MHs. See CA Bus Maps. If you are stopped on a prohibited road it could be a very bad day that involves towing, etc.
Avenue of the Giants is VERY narrow and many an RV gets damaged. Do you have a toad?
We prefer to stay at Ancient Redwoods RV Park in Redcrest. Both the 101 exits immediately north and south are OK to get to this park. We have stayed at Crescent City but not to visit the Redwoods.
Correction: The bus maps show prohibited roads for MHs OVER 40' which includes 199.