Yes, you would need some kind of punching machine to punch out each one.
It would take a lot of man hours to do so.
Edit to add:
If you punch one a second it will take 10 ish days before you even have a recoverable product.
No way anyone will be doing it like this
It would simply go to the furnance for proper burn and incineration. And ashes would be smelted to obtain something metallic to work with. I will be very curious on the composition of the metallic residue - from my experience with plated material it should have measurable gold concentration. Metallic residue from typical close cut fingers is around 10-35% metal, depending on thickness of the boards. And it can easily shoot many % of gold in composition. If you will be able to produce even 0,5% Au bars, it would be then very easy to process.
Also, if there is a filler in the plastic, you are essentially screwed, as from 4 tons or whatever ammount, that will be so huge pile of ashes, it will never justify smelting.
In my wildest dream, what I do... I would try to pair with some facility that incinerates waste, and strike a deal that they will burn it in their furnance (as all their waste) - making pretty nice profit from energy, as 4 tons of plastic is energetic as hell
And in return they will get you all of the ashes produced. Even if they will request some pay for this odd and strange service, you would be better off than constructing the incinerator.
Then, you will crush the ashes to powder, sluice them or froth them in flotation tank to retrieve the metallics (recovery won´t be ideal, but still better than smelting the whole lot of ashes), and from there it should be relatively easy.