I found at least on Ubuntu Linux that I could create a launcher that points to:
I then set the icon to /opt/google/chrome/product_logo_48.png
I then ran this to install sqlite3 (if you don't have it).
sudo apt-get update
sudo apt-get install sqlite3
I then create a Batch script ~/bin/chrome/launch.sh that has this inside:
sqlite3 ~/.config/google-chrome/Default/History 'delete from urls;delete from segments;'
At that point, Google surfs with no browser history except for cookies. However, note that this isn't 100% perfect. As you browse around on the web, it starts collecting more urls. However, at least when you shut down the browser and pull it back up, it will still remember your cookies but have a brand new browser history.
The above might not take that many more changes to work on a Mac because it's based on BSD UNIX, which is similar when it comes to Bash scripts. Also, on Windows, I am assuming one can make a launch.bat file that does something similar if one has installed the command-line sqlite3 command. Note on both Mac and Windows that your profile path may be different than what it is on Linux, of course, so you'll have to change that path.
EDIT: Alternatively, you can simply install the "No History" (the one by "kvsoftware") extension for Google Chrome. It's free and basically wipes out all history as you browse, even when you open a new tab, yet keeps your cookies just fine.