Can I move updates from games to an HDD?

This is definitely not possible, because you can't simply separate an update file from the game itself on a PS4. As Timmy Jim mentioned in the comments, these update files you download and install aren't simply left on your PS4. They either replace files for the game or are added to it (in the instance they're entirely new).

A helpful Q&A over from GameDev.SE explains how updates work quite nicely:

However, most patching systems in the wild take the simplest route: they just package files that have changed - they don't attempt to only package changes within those files (probably for good reason, most game content is compressed already and creating patches against high entropy or compressed data won't work at all).