If you run
git diff > your.patch
The normal git diff output will be saved to a file.
If you take that and apply it to the directory with patch, you'll update your files.
patch -p1 < your.patch
You need -p1 since in the diff output the file name are like
And you only need the 'your/directory/...' bit, so p1 says ignore everything up until after the first slash.
If you want to make backups, issue patch -p1 with the -b argument.