I managed to repair a water damaged machine by sanding the bajeezus out of it, flaking off the rotten wood, and wood puttying the holes. Of course, this is from a machine in an advanced state of rot, so I'm not sure what a freshly moistened machine would do if you sanded the hell out of it.
Is it possible to strip the paint in that area, use a space heater to dry it quickly, and repaint? I think that would work, but I am hardly a carpenter... I think you could prevent any damage (aside from cosmetic) if you just got the wood dried out quickly... No rot, no warping, etc.
Good luck and I am sorry to hear about your cab.

APf