> I would like to laminate wood for a paddle, but I don't want to put any
> finish on the paddle afterward. What should I use?

Definitely do not use carpenter's glue. My brother and I both made laminated paddle shafts with carpenter's glue (yellow) We made 'glass blades and covered the entire shafts with epoxy, but they're still delaminating. Use epoxy and you should not experience any delamination problems. I would advise coating the paddle with epoxy just for water resistance.

If you're thinking no finish for the sake of feeling the warmth of wood while you're paddling, don't do it! Water really raises the grain, and you can then experience the "warmth of splinters"! My paddle shafts are coated with epoxy and a coat of spar varnish. If you're concerned that that will feel too glossy/ slick, just sand the finished shaft lightly, or rub it with a bit of steel wool.

If you want to stay away from epoxy or varnish, I'd recommend linseed oil

Good luck,

Shawn