Listen for rattling raspy breathing and regularly check for weightloss. If they are just sneezing with no other symptoms, I wouldn't worry yet, just closely monitor.
As long as the rats are eating/drinking and have good body condition, and no symptoms (raspy or difficulty breathing/weightloss) they should be fine to continue to breed for food.
If you culled the sick male, you can alternate the other male between boxes, just make sure the females have no pups when you put him in(which should work if your using pups as food).