Sounds like you're more worried about mishandling than you are about theft. You certainly can ask for private screening so other passengers can't see the item. As for mishandling, I'd ask for assistance from the airline. Given that you've mentioned purchasing a second seat, the airline may well be willing to assist.

If you're flying with AA, for example, you might find it worthwhile to consider their Five Star program (extra cost, but they do assist you & escort you through the airport process).