I,ll have to agree with Jim Keenan. Forget the bore snakes. I just got through removing one from a .303 Enfield. One of those cheap take-down clean kits cost lots less than I charge to clear a mess like that.
--As for the wood in the barrel, clean it as normal, with a good brush and clean patch. Since the plug was near the chamber end there should be no accuracy problems. Clean it. Shoot it. And I believe it'll be fine.