I would just ask why they’re pushing it. If they say they simply do not want guys tearing apart their setup to put in timecode solutions, then it makes sense. Ask then if it’s ok you use your controller from just an aux input on the mixer. If it’s just the scenario that they don’t want people disconnecting and reconnecting the decks, then they should allow it.
NOW…if they’re more the smug anti-laptop guys, then I’d either decline the gig unless they let you play as you want, or learn the basics of using CDJs and just straight mix it.