You don't even have any historical evidence that he existed, much less that he was executed by that or any other means. That's because those clowns who wrote your book of holy fairy tales made sh*t up as they went along, and you've taken a page from their playbook. Pilate was not a procurator--he did not govern a senatorial province, he was a prefect in charge of the sub-province of Iudaea, and his only duty was to guard the trade routes to the Mediterranean, which did not include Jerusalem. His administrative center was at Caesarea Maritima on the sea; a dedicatory inscription has been found there which confirms that he was a prefect. He answered to the Legate of Syria--there was no procurator for that province, because it was a frontier province, and therefore was governed by a military man, the Legate.
As a prefect, Pilate had no authority to try or execute anyone. Even procurators did not have judicial powers until the reign of Claudius, after 50 CE. If he had wished to do so, he'd have been obliged to send his proposed victim off to the Legate, along with any witnesses and evidence he possessed. It is absurd to suggest that Pilate would have sent a pack of unwashed, stinking provincial religious fanatics off to the Legate for trial on the evidence of some priests from pathetic little temple of a people who constantly made trouble for imperial officials. Pompey had occupied the temple and used it as a stable just to let the Jews know who was master. The office of high priest was in the gift of the Prefect from a short list provided by the temple. Ciaphas had zero authority with Pilate. The entire story is preposterous.
The completely unwarranted confidence with which you peddle your fairy story is a measure of your delusion.