PU glue is efficient fir this but need to find one that cure “hard”. In France with norms that reduce isocyanate contains homedepot pu glue became white, cure slowly and stay elastic so impossible to sand. The “good” old brown formule that cure as a hard foam is only sold to pro now.
Epoxy foam should be good.
I did a couple of boards with cork rails a long time ago, so my memory about the glues may be off. Some were only cork others were layered 1/8" balsa and 1/8" cork. I used cork from the hobby store or from a school supply store. It was a roll that was 4’ long x 24" wide x 1/8" thick. I think I used wood glue and I also used epoxy, the same epoxy I use to glass. If you use the quick setting epoxy, you won’t have much time to work. I’ve used 60 minute cure but not the 5 minute cure epoxy. I think you could use a spray glue like 3m. My brother had a super glue that we used, but I don’t know what the brand was. I did some balsa work a few years ago with super glue, but a few pieces came apart easily. I also think you need to glass over the cork for your rails, or they will eventually fall apart.
I stopped using only cork because it’s heavy, and it doesn’t sand cleanly. I use either XPS foam because it’s waterproof, or just balsa. I only do between 1/2" and 3/4" wide total for balsa and 1" for foam. The last few wood boards I did were hollow balsas, and I used wood glue. They were glassed. I don’t do many wood railed boards these days, mostly deck skins over EPS and the skins don’t go all the way to the rail.
