Never use stainless:
[youtube]pzV6J3SQ8Qs[/youtube]
There's two options I can think of:
1) Get a katana custom-made out of SM-100 titanium alloy. It can be hardened to the Rc 60 range and I believe can still be bent to a 90 degree angle and still bend back to its original shape. Though to be honest a lightsaber would probably cost less

. But this baby won't rust on you.
2) Have the blade custom hard-coated, preferably with DLC. Would still cost you a pretty penny, but probably less than option 1.
You can attempt to coat the blade with something like Eezox, but I doubt any such coatings are meant to hold up after repeated contact with solid, possibly abrasive mediums like bamboo.
Short cutting shouldn't affect the blade, but if you're doing it in the rain for hours, then it wouldn't be surprising.
Only realistic solution I see is that you get comfortable with taking the katana apart and putting it back together again. After each use, take it apart, clean the blade with rubbing alcohol, polish the rust out with Mother's Mag & Aluminum Polish(best and most aggressive IMO), clean the blade with rubbing alcohol again, and oil it. May want to apply the same treatment to the iron hardware, but Eezox and similar protectants should work well on those parts(because you're not cutting with those). The wooden handles should be dried out and (need expert input here) probably sealed up with Renaissance Wax.
Basically you'd be polishing the rust off instead of trying to prevent it from forming during use. It'll mess with the finish, but I assume that's not a big consideration for a user.
Honestly though, if I expected to do cutting in rainy conditions, I would NOT use any organic materials(specifically the wood handles), and I would make sure the handles are either easy to take apart, or outright sealed off with epoxy.