In short: Is there a way to disable storing full history for specific folders in git-svn repo?

We have pretty large SVN repo with big checkout. I would like to migrate it to Git for my local development, because Git speeds up update and status commands orders of magnitude.

When I simply do git svn clone it creates very big repo. Big enough to be bigger then my whole HDD. The problem lies in binary directories for which history is too large.
Latest binaries are required for proper local build, but history is not required at all for my development process. I will never change them myself.
I would like to store only latest versions for specific folders, or may be a history, but for no more than a week.

I could only found filter for git svn fetch, which excludes specific folders at all. This is not exactly what I need.

It's OK with me to have Cron task which deletes history from specific folders, but I do not know how to make one. Also Cron does not solve problem of first git svn clone.

P.S. SVN repository structure could not be changed by any means.