Whatever you do DON'T check it! Traveling with multiple laptops isn't a big deal. I've done it many times. I wouldn't wrap it just in case the TSO at the x-ray decides to be a d-bag about it. You'll need to take it out of your bag and run it through like any other laptop even though it's in its shipping box. If you're traveling with someone I would *highly* suggest you let a few people go between you so they can stay with the laptop while you're being screened so it doesn't grow legs. If you're by yourself it might not hurt to befriend the person in front of you and ask them if they could keep an eye on it for you. of course they could snatch it but that's unlikely.

There's a chance they make you open the box if the charger and other stuff in the box prevents them from seeing the laptop clearly. If it was me I'd just carry it on even if I end up having to open the box. Then again both times I've given a laptop I've opened the boxes to charge them and move the data from my grandma's old one to the new one.

I'm sure the more experienced FT'ers will chime in but that's what I'd do.