2 part epoxy and screws would probably work. However, traditional kayaks were just lashed, no glue, no fasteners. Most folks use atrificial sinew these days and it worke very well. SOF kayaks are pretty flexible, so lashing works very well ans screws and glue make real stiff joints that attract more load. Consider ditching the glue and screw ffsteners for lashing.
TThere are several book that detail lashing patternes and methods: kayaks of greenland, Chris cunninghams book, etc.
Seal all of the exposed plywood edges with epoxy as open plywood end grain acts like a sponge and plywood rots out rrather easily.