I've not used it specifically on wood smoke odors, but I've used it on everything else I can think of. Try a 50/50 vodka and water mix in a spray bottle while your hammock is airing out. It's my go-to when trying to remove odors from any fabric.
Just pick up a cheap bottle of vodka, mix and spray!
Better yet if you drink all the Vodka you wont care what your gear smells like