That is a nice cruise. We were on Infinity in Dec 2016 but we embarked at Valparaiso. Your idea is a good one as that area is worth exploring and you don't want to simply rush off to SCL only to wait for the majority of the day. You will need to decide what you want to concentrate on as there is simply too much to do and see in the short time that you have.
You should be able to find a company that will conduct a private tour that will pick you up at the cruise pier and drop you off at SCL. Because my situation was different, I have no recommendations for you. However a cursory check of the internet shows that those services are available. Here are examples: link and link.
Good luck.
Infinity docked at Valparaiso, Chile, Christmas Eve 2016