When I'm on the go with my nebs, I always just bring a bottle of water with me and just rinse out the neb pieces when I'm done. Then when I get home I do a more thorough cleaning job.
As far as the afternoon dose of Cayston goes....my clinic has decided that compliance is VERY low with the afternoon dose of Cayston and has recommended that we take 1 vial in the morning and 2 vials at night (versus the standard 3x/day). I know this isn't the way the drug was 'approved', but it is the standard way to use Cayston at my clinic. Could you maybe recommend this option to your doctor?
Let me tell you, before I switched to the 1 vial morning/2 vials night, I was unintentionally forgetting the afternoon dose ALL the time. It was like my brain wasn't wired to do treatments at that time of day. Not only that, but sometimes finding the time to fit it in was ridiculously hard. It really cuts into your day because you have to stop whatever you're doing and re-arrange your life for this 3-minute treatment. Sort of annoying. So let me tell you, I totally feel your pain and I'm sorry that you have to deal with Cayston at the same time you'll be on vacation.
The other option is, that perhaps by the afternoon, you and your family will be ready for a break from Disney and you can all head back to the room for a rest, and then you can fit in your treatment then. Then you can go back to Disney afterwards and enjoy the rest of the evening there.
I'm sure it will all work out for you. Enjoy your trip!