You'd - in the first instance - open up a copy/view a video and see where it says "copyright xxxxx" and contact that company/individual. Because if the copyright has passed to another - they will know who now holds it.
But as far as I know if it is ONLY for your own use and you are only making a single copy - you are pretty much OK. Make one more for a friend and you are liable for a lawsuit. This was discussed here somewhere in terms of the idea of making a single birthday card using an on line or photocopied tarot image - you are OK, whoever knew their stuff said - until you give it to the other person... because then it is no longer for your personal use, but for theirs, and
they didn't make it. But if you CUT OUT a tarot card from a deck, and stick it to a card and send that - you are OK because you owned the card, like.
I have to say that as far as I know, no-one generally gets permission to use what you might call commercial characters. Think of Hello Kitty - where Rosales has been sued all over. They have now brought out their own, far inferior deck - they slipped up; they should have bought his !!! Peanuts, too. That was a GREAT deck
You've nothing to lose by asking though - how long does a letter take ? And Kripke is still a producer, so I imagine he has some considerable say. (From wiki, BTW, I would guess Warner holds it now... as they partly own CW too, but that is a guess.)