If the area is not too too large and the plywood is still in good shape I would remove the interior skin and place a dehumidifier inside, seal up the cabin, and let it run for two weeks or so. They work better than a heater and you may find that the removal of the wood is not necessary at all, assuming that it is still well attached to the outer skin.
A friend was able to dry out the interior of his West sail 32 in this manner and found everything in good shape and ready for re-finish. It is certainly worth a try before you really know if a re-core is necessary. He also discovered in this process that he had termites, due to the wet wood. They, the termites, dried up like grains of rice and covered all flat surfaces.