Andy’s tunnel to freedom was already completed by the time of Tommy’s death. There was no need to bring the matter to the warden. Even if Andy’s conviction had been overturned, the hole would have been discovered once the poster was taken down. How did he think that would have played out?
shareThe murder conviction still would've been overturned at a new trial. Yes, he may have had some charges of damaging the prison or trying to escape but the murder charges still would've been expunged from his record. After the 19 years he spent in prison as an innocent man any possible charges of damaging his cell, or the escape attempt would've been been sentenced as time served and he'd be released a free man, without the need to go to zihuatanejo on the run for life.
shareMatt above has the right answer: he would be far better off being legally cleared of the charge of murder than use the tunnel in an iffy escape attempt.
What the movie doesn't address is what Andy's plan would have been for the money if he was legally cleared. Would he still be able to steal the money and get the warden in trouble if he hung around? How would he explain his involvement?