Well, I guess that depends on your definition of an "Old Town" wooden kayak. In 1940 and 1941 some of their catalogs included an insert for a wooden kayak as shown below although one could argue that this was just a short canoe with long decks. Kennebec and other manufacturers also offered similar kayaks during this period.
Old Town also listed a fiberglass surf kayak in their catalogs from 1971 to 1978 that had an "end-grain-balsa-sandwich hull" as shown in the second picture below.