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.