How well do Eppendorf cups seal?
I have never had  problem with tubes leaking. However, if you are worried about them getting somehow popped open in transit, you might consider wrapping the lid in parafilm. Alternately, there are lid locks that you could use like these.

@Chris has a good point about screw-cap tubes, they could also work, and are probably a lot sturdier, in case of actual damage.