An owner with the handle "Mathurin" posted a lot about repairing the deck and cabin core a few years ago. Some of the links he posted are in the "H37C Knowledge Base" sticky at the top of the Cherubini Hunters sub-forum...and some of the links are broken
but here is one that works and gives some info:
H37c Porthole Rot Fix (Updated)
There is also some info (in French with some English - scroll down) on the Mathurin II blog:
Les rénos
The core is indeed marine plywood and is generally ~3/4". In some places, like around the mast and at the aft end of the cabin, there are aluminum plates bonded in (for attaching winches, cleats, etc.). If the area is small, you may be able to get away with injecting epoxy, as described in the West System epoxy manual. If the area is larger, the best solution is to carefully cut off the outer skin, remove and replace the damaged core, and re-glass the skin, fill and paint.