You can purchase a "lead" lined flexible bag to protect your film and disposable cameras. They are not very expensive and you can find them at camera stores. Then everything can be x-rayed and your film won't get fuzzy.
The xray machines for the "sent through" luggage is much stronger than the xray machines for your carry-ons. So far....none of my film has been ruined by putting my film in the carry-on and having it go through that machine. The film in our disposable cameras has also not been affected...neither the underwater kind nor the regular disposable.
As already mentioned, carry on screening is much lower power than those used in checked baggage. Lead lined bags will not always work and will guarantee your bags will be opened and hand checked after going thru xray, since they look suspicious. Asking for hand checking for all film both shot and unshot is the best way to go and putting in carry on is the second best. The impacts of doing this add up so don't put more than you need thru unnecessary checks.
Disposable cameras are plastic, so I just put them in my pockets as I go through the metal detector. Ship security absolutely refuses to hand check them unless you have 800 asa or higher. I've thought about the "lead" bags and used them years ago - pre 9/11 - when I did photography. (Now I just take pictures,) But doesn't the screener get a little jumpy when they see the a solid oblect that's hiding something? I mean, you could put more "bad stuff" in one of those bags . . .