The problem with that is it is really hard to stop the knife motion with a whizzer. Once you overwrap, you cannot pin his arm so tightly that he is unable to articulate his lower arm and wrist. Generally, the attacker has the ability to keep pumping that knife into your body. And now, depending on how you do the whizzer, he may now have a direct pipeline with the blade into your kidneys. Or worse, do the insert and pull technique.
Also, he still has his other hand free to block/intercept your eye gouges. He is not going to just let you do that and will most likely use his hand offensively as well. Perhaps even try to eye gouge the good guy.
There is no one perfect answer to what to do, contrary to the typical martial artist or combatives instructor's advice. There are a couple of decent strategies to try, but they must be worked in a FoF/sparring situation under heavy pressure to find out what is going to be the best bet in the moment.