Hmmmm...can't you just put the little bottle of plastic drops in your top (bra) and bring it on with you? Then again, if they caught you pulling it out, you'd probably get arrested and then you'd have a new set of problems.
I know this is the world we live in now, sad but true. It's unfortunate, but something we have no choice about, and if it is safer, or even if it only makes us feel safer (don't even get me started on what you're allowed to check in vs. what you can carry on board-like something in checked baggage couldn't be used to do bad things), then it's OK with me.
Hope your eyes don't dry out too much! Have a safe flight!