When you move them to a cheater queue, they don't know. They keep playing, none the wiser. It's infinitely better for everyone. The cheater still gets to play, and the non-cheaters aren't affected as much because the cheater doesn't just keep coming back.
The complexity in your app is that you need to have multiple matchmaking queues, which you probably already support due to skill tiers. So is it really that difficult to add more matchmaking queues for the cheaters?