I have 2 doors in a club house sauna room. The seam from the sauna creates a moist environment. The paint is pealing off the casing and the doors are swelling. I am going to change out the door slabs and repaint. I want to seal everything like furniture. Will this work.

Only as long as every surface is completely covered... including mounting holes etc...

Until you get your first scratch or crack and then moisture will get in and do this all over.

This is why Teak is generally used...

But then you now would have whats likely to be a very hot surface against the skin...defeating the purpose of wood...

Most saunas have unfinished wood, normally teak or heart red cedar

Suggest you consider PVC casing and trim.