I'd take out the bottle, and put in your baggie with the rest of your liquids, and the empty wet box in your bag.
I always put my juices in my liquids baggie, and leave my e-cigs in my purse. I am usually not stopped by security, but I was stopped once on my most recent flight.
They stopped me because of the e-cigs in my purse, not the
juice. They asked what it was, I told them, they re-scanned it, and sent me on my way. It was pretty quick.