John, you said you already had the wood… consider that the original wood handle lasted how long? And, it was likely a maple, birch, beech, etc. type of wood.
If you are open to changing your wood selection, I was thinking of N. American woods used in watery environments:
white oak is traditional for wine making and old ships;
cypress was often used for water wheels (and it grows standing in water);
osage orange for fence posts;
the walnut family heartwood has very good decay resistance when logs have sunk to the bottom of rivers.
That said, I have a number of wood cooking utensils from Big Leaf Maple, Black Walnut, Elm, and Cherry; they all go through the dishwasher
eek
and have for many years now. Not a one has cracked or shown any adverse effects.
I think just about anything would work for your pan handle with just a little conscientious care - and I’d leave off a film finish. The old mid-century red painted wood handles all seemed to show finish cracking and crazing.