You can't use that way of repairing a club construction, the core used is not hollow and is too thin.
As you said, just sand the gelcoat back to expose the fiberglass and repair from the outside with one layer of carbon and then finish off with gelcoat once cured.
To make things easier, use peel ply over the repair and then compress the repair whilst still soft with a layer of masking tape over the whole repair. This will make it quite smooth and when you remove the peel ply it will be ready for gelcoat.