The problem with this view would have to be the ancient sources. Clearly, the death of Jesus was a primitive Christian belief (1 Cor 15) which is multiply attested to throughout the New Testament documents including the Gospels. Even the 2nd century apocryphal texts are certain of this historical fact such as the Gospel of Peter (early 2nd) and the Epistle of the Apostles (mid 2nd century).
So to today's quote:
"The fact of the death of Jesus as a consequence of crucifixion is indisputable, despite hypotheses of a pseudo-death or a deception which are sometimes put forward."For an audio interaction between myself and a Muslim making the claim that the early Christians did not believe Jesus to be crucified:
Gerd Ludemann, What Really Happened to Jesus: A Historical Approach to the Resurrection. p.17