With the exact same design, I think it won't work.
In the box, the contact on the negative side is made with the outer casing of the battery, and in this instructable, the outer casing is... wood.
It could work by changing this feature, but you would have to find a dowel the exact same size as the original battery, so the contact is made precisely. Plus you would still want to have the positive side at one end, in addition to the negative side all around.
Edit: Also this :
You’re basically done. Drop you’re new batteries into your device, make sure the batteries are plugged in, and power up. It should work. If not, check that you have the proper voltage and current going to the batteries for your device. In fact, check that first. It’ll save you from burning a $50 digital camera by feeding 9 volts to it instead of 3 (accident).
You would have to find a proper adapter that will be suitable for the box.
From vaporpedia concerning the AC Power Adapter : "The adapter is capable of delivering a fully regulated temperature compensated 16 amps at 1.42 volts."