There will be a cost yes, but depending on your use case and volume it might not be that expensive. You would only need to run the worker on URLs that are likely to receive Origin request headers, reducing the cost exposure.
I presume the reason you want to eliminate the Origin header from the cache key is that you already issue a Access-Control-Allow-Origin: * response header, and you want to reduce the volume of traffic to your origin server. In which case it is a trade off between the cost of the worker, and the cost of serving this content from your origin. I would have preferred that the Origin cache key was presented as an option in Page Rules, but that will probably never happen as workers can meet that requirement.