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File versioning based on shallow Git repositories?

Can I use a shallow Git repo for file versioning, and regularly purge
history older than e.g. 2 weeks?  Purged data MUST NOT be recoverable.

Or is there a backup tool based on shallow Git cloning which does this?
Push/pull to another shallow repo would be nice but is not required.
The files are text files up to 1/4 Gb, usually with few changes. 

If using Git - I see "git fetch --depth" can shorten history now.
How do I do that without 'fetch', in the origin repo?
Also Documentation/technical/shallow.txt describes some caveats, I'm
not sure how relevant they are.

To purge old data -
  git config core.logallrefupdates false
  git gc --prune=now --aggressive
Anything else?

I'm guessing that without --aggressive, some expired info might be
deduced from studying the packing of the remaining objects.  Don't
know if we'll be required to be that paranoid.