Gasoline.

Great question, any sorta sticky situation def creates issues when doing the fastest trick in the west move

I have an alternate method for all this, I know this is a old thread but I feel this is a neat way to handle the issue if you want to keep the tab, but not risk getting glue on cards.

You need a new box and invisible tape (sometimes called gift wrap tape), just make sure it looks matte finish so it goes on invisible.

1. Cut the seal along the fold.
2. Tip box backward to let the cards come out without touching the sticky tab.
3. fold over what little bit is left (or trim off) the semi-circle side of tab into the box.
4. Use invisible tape on the outside, and leave enough to flap over onto the inside to cover the rest of the left over tab. Take the time to make sure both sides are 100% flat. (keep flush with top of the front of the box.
5. You can also use a small piece of tape to completely cover the top of the deck box's sticker to make sure that does not start lifting.

It takes less than a minute, and I feel it beats putting chemicals or cleaners on the box to get clean.