I have successfully used Titebond II for years.  To build the stripped deck on my new Woodduck Hybrid 10, I purchased a bottle of Titebond III which is labeled as waterproof.  After a half hour of glueing strips, I was pleased with the rapid bonding and less yellow color of the glue.  Then I tried to wash the crusty glue off my hands.  It took 10 minutes of scrubbing with abrasive hand cleaner and the green abrasive side of a Scotchbrite heavy duty scrubbing sponge to get the glue off my finger skin and nails.  The label says, "water clean up."  In reality cleanup must take place within 5-10 minutes of using the Titebond III.  Now I always put on nitrile gloves before picking up the Titebond III bottle.