I can't advise re the wood species to use (or not)? But re waterproof glue, a GOOD quality slow-dry 2 part epoxy will definitely do the job, and will in all probability outlast the wood in the situation you describe.
Examples: Araldite (the original), needs at least 24 hours to fully cure and is then impervious to just about anything short of a nuclear holocaust. Or West Systems - similar comments to the above except usually a bit quicker to cure (but check the specs before buying, there are several different formulations for different applications). And another down side - both relatively are expensive (but you won't need a lot).
BTW: It often surprises me how often many people on here have doubts about "glue" (various) in various applications. IME, most people who experience glue joint failures have either A) got gaps that are too big in their joints; and/or have failed in the scrupulous cleaning before glue up bit (e.g. ALL dust, moisture, oil - including finger prints - etc, etc - GONE)!
Aside: If you haven't already done so, the next time you fly away on holiday it will be in an airliner that has, to a large extent, been "glued together", mainly using 2-part epoxy VERY similar to the above. Despite what you may read in the news (e.g. Boeing 737 Max) structural failure due to "glue failure" is virtually unknown these days, unless due to a QC oversight during manufacture or external "aggravation" of some type (like getting bashed by a baggage trolley while on the ground).