Sublime-merge (the Gui git client from the sublime text people) is available in a portable version, and so can be run as a .exe from the filesystem, or a mountable drive. Comes with its own git binary.

The GUI is stunningly beautiful and functional, and there are more than enough keyboard shortcuts to keep things snappy once you're in the flow. I used to live and die by the terminal, now I am in love with sublime merge.

I used the portable version for a job where I didn't have install rights to the corporate laptop, and it preserved my workflow and kept me sane during my dev work. The portable version can run a little slow, but it's a pretty good solution.

I'm in a similar situation and the entire git for windows setup (including git bash that works beautifully with things like Windows network drives!) can be used without ever needing admin privileges. So I not only have git but also vim and perl and the whole *nix kit I was so sorely missing.

Some truly locked down environments may not allow it but if the poster has other open source tools like R they can probably run .exe files.