I deleted my first post, as I changed my mind.
Air Lock was my original vote, but I decided that I want to vote for no second ability. It was not a very difficult decision to make. Air Lock just does not fit right. Yeah, it helps counter Tyranitar like I originally intended, but it just does not fit a mummy. Plus, a mummy would not want to stop a sandstorm ...
One of the neat things about Shed Skin is that it helps, well, shed status, including the likes of sleep after using Rest. With Sleep Talk, this could come back to bite you, but it also allows for a set actually void of Sleep Talk, altogether.
Insomnia is the exact opposite -- while it would be cool to avoid sleep, altogether, that would mean that it cannot use Rest. This thing wants to survive to take on Heracross and company for the whole match. And, without Pain Split, a move to which it very well may not have access, it needs to be able to sleep itself.
Dry Skin is neat, but the more I think about it, the more it is overpowered. Suddenly, this would become a Gyarados-killer, bulky water-killer, and an overpowered Vaporeon with access to some excellent resistances. Plus, it does not exactly fit the description of a mummy, in terms of absorbing water attacks.
Snare Trap, honestly, I really just do not like it all that much, and I want to stray away from needing to create a custom ability for every Pokemon that we create.
So, no second ability it is.