Yeah, it's just simply put all cards out and put the box in and add card one by one carefully. Then use the new seal to seal it. But this way cellophane must be ripped off.
If you simply opened enough of the cellophane, you could leave the tuck box mostly wrapped. It would also give you a chance to remove the original deck seal and replace it with a new one, assuming the deck had a seal.
If you opened the top and bottom of the cellophane, you could fold the box flat and curl it to fit it into the bottle, then flatten it out and reform the box, regluing and resealing the bottom while inserting cards one or two at a time through the top.
It requires some LONG tools for the detailed manipulation work...and probably more patience than most humans have these days.