Assuming the deck/coach roof is not 100% cored with wood to the inner linner, I am trying to find out where there might be solid fiberglasss.
It is all cored with either balsa or plywood, all at 0.5" thickness.
Specifically, the plywood base to the cockpit cubby holes extends forward to form the deck core to more or less the front of the cockpit, it also extends aft to the transom. The cockpit floor is all balsa, but around the rudder stock there is an extra layer of 0.75" plywood glass under the deck. Under the aft inner shrouds, where they attack through the deck, is an area of plywood coring. Under the mast the core is made from strips of plywood, and for a few inches either side.
You can either work on it from above or below. If you have fairly large areas to work on, your original idea of cutting around the non skid areas is probably the best bet; working from above has the advantage of your rebuild staying where you put it while it sets, rather than having to hold it up inside, plus you will leave the headliner intact. If it is just a small area, Steve's suggestion of working inside may work out better, so you will not have a blotchy deck to worry about.
Technology has moved on since 1974, take a look at this for a new coring material:
http://www.diabgroup.com/americas/u_literature/u_pdf_files/u_ds_pdf/H_DS_U.pdf
I used the Divinycell H60 for the new core, except where extra strength is required (under the mast or wincehs etc), where the Renicell E320 has the required tolerances.
It is a big job to start out with on your new boat; it is also fairly common for balsa decks to get like that. But you have got yourself a great sailing boat, once the work is done.
Gareth
Freyja E35 #241 1972