Yes, you could redirect them from the end of the main survey into another form/survey where you don't link the results. However, it wouldn't assure anyone that it is anonymous, because you could link the data that way. It COULD assure you that no one internally in your organization would link the data, which may or may not be a concern.
If you do that, though, technically they could complete that last prize draw part multiple times with different email addresses if they're clever (because you aren't tracking their unique IDs). It probably wouldn't happen though, because they would need to understand how the links work, not to mention use multiple different email addresses (otherwise you could just look for duplicate email addresses).