If your tenon is a snug, but not a tight fit (you may snigger, but not sneer, please), would you use a nornal PVA wood glue, or something with a bit more body? Like Araldite, maybe. The timber is seasoned oak.
yes as the builder says polyurethane and it is aqua water proof you need to assemble quickly though.
Cascamite is another good one also water proof.
hth Tez