You can get bags up to ~44L or so that are airline carryon compliant. A bigger problem is the weight restriction of 7kg, which is rarely enforced ex-USA, but are often enforced ex-elsewhere (particularly Oz & NZ)
I haven't had good luck with locking checked bags in the US, so I wouldn't worry about it. Climbing equipment isn't high on thieves list, and TSA has trouble even with the TSA approved locks. Go to REI or the like and spend $20 on a cheap Outdoor Products duffel and don't worry. When you get to S. America if you are travelling domestically spend the $7 on shinkwrapping your backpack or $5 on a padlock.