The theory that Jesus was never placed on the cross at all, but that some substitute was crucified instead is a more popular theory than the swoon theory. There are a number of candidates for the person substituted but there is particularly convincing evidence for none of them. For example, consider the possibility that the person crucified was Judas. The evidence for this is from the Gospel of Barnabas, but this is a late medieval forgery and cannot be relied on even to get the geography of Israel correct, let alone the details of the crucifixion. All the candidates for a substitute suffer this same problem of lack of evidence.
One thing that is certain about the events of Passover 30 AD is that someone whom the authorities believed to be Jesus was crucified. The evidence for this is very strong. Not only do all four gospels mention the death of someone on the cross (identifying the person as Jesus) but Jewish sources and Roman historians also give witness to the death.
One of the Barioth says:
On the Eve of the Passover they hanged Jesus ΠBaraitha, Sanhedrin 43a)
Tacitus says:
“Christos, the founder of the name [Christian] suffered the death penalty in the reign of Tiberius by sentence of the procurator Pontius Pilate and this pernicious superstition was checked for a while, only to break out again” (Tacitus, Annals 15:44)
Another indisputable fact is that the tomb in which this person was buried was empty on the Sunday following the crucifixion. Again, this is without any doubt. The tomb was near Jerusalem and anyone who wished could examine it. The Jews consistently proclaimed that the disciples had stolen the body, a ludicrous claim if the tomb was not empty. Neither the Jews nor the Romans were ever able to produce a body, something that it would have been very much in their interests to do as it would have put an end to Christianity very early on.
The substitute theory fails to explain the empty tomb. Whoever was crucified must have been buried afterwards. Within three days the tomb where they were buried was empty. Where had they gone? Had God raised the substitute from the dead? Why should God raise the substitute from the dead when he was not prepared to raise his own Son? The substitution theory provides no answer to any of these questions.