That being said, the crucifixion had nothing to do with sin.
"If a wicked man turns from all his sins which he has committed, keeps all My statutes, and does what is lawful and right, he shall surely live; he shall not die. None of the transgressions which he has committed shall be remembered against him; because of the righteousness which he has done, he shall live." - Ezek 18:21-22
Even according to the Old Testament, if you turn away from your sins and does the right thing, God will not hold the sins against you. The verse is so clear that I cannot understand where people get the idea that God wants someone to pay for all our sins.
And once you've got all this "payment for sins" stuff out of the way, there is no good reason why God couldn't have made it look like they crucified Jesus when they crucified someone else, like the Muslims believe, except that such an approach seems very deceitful and I cannot imagine God playing tricks on people like that. If he really wanted to save Jesus from the death on the cross, he would have made it very clear, not deceiving the ones who wanted to kill Jesus to let them believe they did. Why would God let the unjust believe they won?
And just to clear it out the way, there is no way Jesus would ever have been let off the hook by the Romans. We know from historical evidence that it was Pilate who was in charge at the time and that he was a ruthless person (the Biblical image of him is just so wrong). There is no way he'd let the leader of a rebellious movement like Christianity live.