I use a similar set-up as you, and you need the sound card to process the timecode media. I don’t think the mixer will allow you to control the CDJs as they are quite old.
In this case, you could just connect the 900 Nexus mixer (if it has USB? I’m not sure?) and play without the CDJs and use sync if you have to. Or maybe another DJ playing there will have a sound card you can borrow – or one of your friends perhaps ? Just curious, why did you buy Traktor Scratch Pro and not get a compatible sound card?
Also, why would a venue buy a Nexus mixer and use CDJ 1000s š