Woodworking in a shower requires the use of some very strong waterproof woodglue! This is why I use Titebond III.
I used this woodglue to build my first wooden dinghy (Tooth II) and while the dinghy itself was far from a success, the parts that I glued were. The transom of the dinghy was made out of edge glued Douglas Fir that was glued together with this very woodglue. While most of the boat leaked, that transom was watertight and solid as a rock!
I have had the misfortune of needing to separate pieces of wood that I erroneously glued, and I can tell you, the glue line did not fail, but instead one of the pieces of wood tore out of the plank! This glue is waterproof and permanent! But, while it is still wet, you can wipe up drips with paper towel and water. The glue is also not toxic to your skin and has no respiratory warnings (unlike other waterproof woodglue).
If you ever need to glue something out of wood that will live above or below the waterline, this is the woodglue to use!