Thank you all for your wisdom. Some added insight from my part:

1) I bought the razor from a third party seller who said the rusting must have happened when I shaved. That is, water droplets stayed on the spine and voila. Does that even make sense? If a blade is *so* sensitive to water and has trouble in a 15min shave, then there must be serious manufacturing issues, no? Or the seller had improperly stored the blade and just sanded it before shipment. Which brings me to my second point.
2) I sanded the spine with 1200 grit paper and removed the rust.
3) My second shave I did see water droplets sit on the spine. I did nothing about this and at the end of the shave I had to sand again. Gah!
4) Lesson learned. While shaving, wipe any droplets that stay in single spot for a prolonged period of time.
5) I use the Hart Steel oil that was given with the unit after wiping the razor post-shave and store it for 2-3 days before my next shave.
6) No issues up to this point (on shave 10+ currently)

As much as I would love to leave it someplace safe to air dry, its just cumbersome for me. In addition, the Hart Steel oil has worked fairly well after an initial wipedown. I will see how it goes. If the oil is trapping air, I'll switch to the oil suggested above. As for the wood, I haven't done a water test, but I do the inside of the scale after my shave too.