Yes, you can install just the Fixpack. It's designed to be installed first either way since most of it consists of major bugfixes.

(Even if you don't want the extras, I would still highly recommend installing the Tweak Pack as well, for the Banter Accelerator component, which even the modder himself was considering putting into the Fixpack instead. You can choose to select the components you want on installation, so you don't have to apply all of the recommended tweaks if you don't want to.)