Both veterans missed practice Wednesday and Thursday with high-ankle sprains, while McCoy again took the first-team reps.
McCoy had a relatively successful NFL debut last week against the Pittsburgh Steelers.
The third-round pick threw for 281 yards, one touchdown and two interceptions in a 28-10 loss.
The Browns will get another chance to evaluate McCoy in New Orleans. Cleveland (1-5) then has the bye week to determine whether it will stick with the rookie or go back to Delhomme or Wallace in two weeks.
James Walker covers the AFC North for ESPN.com.