Yeah inget the motivation behind exciting the switch. The question I have is what is the motivation behind having the box on the table. Because you cannot remove the cards from the case. You have to start off with the cards out of the case. So it makes little sense to me why I would pull the deck (inboxed) out of my pocket, then remove the case out of my other pocket and place it onto the table, only to then later pick up the "empty case" and place it back into my pocket. Maybe I am reading too much into it, but it feels like so much more work thank just performing a gimmickless switch under misdirection.
Surely the whole point of the cooler is that the card box is an 'uninteresting' item. Therefore, there is no need to justify it's presence, as no one cares it's there. You have cards in your hand so why wouldn't there be a card box on the table? If people notice it, they know why it is there and then quickly dismiss it as you should be doing something more interesting anyway. Chances are most people won't even notice it.
I don't own a Cooler, but I do know what it is so understand your point about not being able to remove the cards from the box. But here's an idea: How much attention do people really pay when you remove the cards from the box? Have the cooler, loaded with your 'cold deck', in your pocket and you regular 'warm' deck just behind it. Whilst chatting, reach into you pocket and remove all of it in the one hand. Slide the 'warm' deck out from behind the box and then place the box, with the cold deck inside, on the table without paying any attention to it. I must stress that you don't in anyway need to pretend to remove the deck from the box, but given people aren't really paying any attention at this point anyway that is what they will remember.
And if they do notice the deck came from behind the the box? Well, maybe that's just because when you left the last group you were performing for you just chucked the deck in your pocket next to the box instead of putting it away properly, and maybe you just pulled everything out because it is easier than fumbling trying to just get the deck. This justifies bringing it out for no reason (as you only brought it out because you 'had to' to find the deck) and also justifies you putting it away, as the implication is it shouldn't have ever been out in the first place.
I'm not sure if any of the above make sense, but hopefully you can decipher it!