Upon a judgment of death made by a judge, it shall be the duty of the judge to sentence the defendant to death and to indicate the sentence in writing, which writing shall be filed with the papers in the case against the defendant. A certified copy of the sentence shall be sent by the clerk of the court in which the sentence is pronounced to the defendant's attorney of record, to the Attorney General, and to the superintendent of the state correctional institution where the execution is to take place, not less than ten days prior to the time fixed in the sentence of the court for the execution of the defendant. In all cases it shall be the duty of the sheriff of the county in which the defendant is sentenced, together with one deputy or more if in the sheriff's judgment it is necessary, and provided that in all cases the number of guards shall be approved by the trial judge or, if the trial judge is not available, by the judge of the probate court of the county in which the defendant is sentenced, to convey the defendant to the appropriate state correctional institution, not more than 20 days nor less than two days prior to the time fixed in the judgment for the execution of the defendant, unless otherwise directed by the Governor or unless a stay of execution has been caused by an appeal, granting of a new trial, or other order of a court of competent jurisdiction. The expense for transporting the defendant to the state correctional institution for the purpose of execution of the death sentence shall be paid by the county governing authority of the county in which the defendant was convicted, out of any funds on hand in the treasury of the county.