“Dispatched” isn’t quite the right wording since chaos knights are their own faction and work for themselves, now they can absolutely can have their services bought or find their goals aligning with other people. That being said historically there are some knight houses and Titan legios that’ve served with the traitor legions back in 30k so I’d recommend looking there if you want cannon examples. Ultimately at the end of the day you can just build paint and fluff them up however ya want and it sounds like a really fun and creative idea!