I would never travel with Clorox myself, personally. I had one accident when I was driving home with some clothing I had just bought and I put some groceries in the back of the car too, and I didn't notice that the Clorox-containing bag had landed on top of the bag containing a new red sweater and some other stuff. By the time I got home after an unexpected side trip, the Clorox had been leaking out of the bottle and all over all the new clothes. Not only did they look like a weird tie-dye experiment gone horribly wrong, the Clorox had physically damaged the fabrics and frayed areas / holes had started to appear. That was pretty upsetting, since I never got a real chance to wear those things.
As far as traveling with Clorox, I highly doubt that security would let you anywhere near the planes with such a dangerous liqued in your suitcase, and I think that you shouldn't take the risk of ruining stuff that way. I had one of those leg bags myself when I was in a major accident when I was a teenager, by the way, so I understand about them.
Have you tried to get a hold of someone in the housekeeping department? I mean, those who clean the cabins and everything else on the ship. With all those people on board, I'm sure that they would have tons of their own Clorox and may be willing to just give you some out of their supply, since you probably wouldn't need much and they would most likely have literally gallons of it. I hope this idea helps, but I don't know if the customer-service people would be able to tell you if the housekeeping (I don't know their preferred term...) staff would let you have some of their bleach (it may be an industrial variation of Clorox, but it should work just fine) so if you can find a way to get ahold of someone actually working in that department they should be able to help you out. (if you say that you have a small medical device that needs sterilizing or such, I would think that they would be even more willing to help you out instead of just humoring someone who wants bleach to clean the bathroom sink again or whatever).
I worked in a hospital in the housekeeping staff as a summer job when I was 16, so I know industrial cleaners are really good, even if they're not the same kind of stuff in the grocery-stores.
I'd like to know what you find out, and again, I hope this idea helps. Tara