The Gemara in Kiddushin that refers to Eisav as a mumar does not specify which type of mumar he was. I suggest that perhaps Eisav was considered a mumar leteiavon, and not a mumer lehachis. Therefore, if someone else would check his knife for him, he would be allowed to shecht. Yitzchak knew that Eisav was outstanding in the mitzvah of kibud av (honoring one’s father) and he was certain that Eisav would fulfill any of his requests. As a result, Yitzchak told Eisav now to sharpen his knife in order to be certain that he would check the blade. Yitzchak felt that the level of certainty whereby he knew that Eisav would follow his command was sufficient to ensure that the knife was checked – as if someone else actually checked it. Thus Eisav – a mumar leteiavon– was permitted to shecht.
Although Yitzchak had reason to be concerned that Eisav would not check his knife on his own since he was a mumar leteiavon, he nonetheless knew that commanding him to do so would be the equivalent of someone else checking his knife for him. This permitted the meat to be eaten. Based on this, we can also answer the question that the ba’alei Tosafos asked (how Yitzchak could have eaten from the shechitah of a mumar). Since Eisav was considered a mumar leteiavon, once his father commanded him to check his knife his shechitah was permitted.