Logitech's best kept secret is they do make a lightweight version of their software for exactly that, it edits the settings saved on the mouse and does absolutely nothing else. It's only available for Windows though.
Logitech's mice can't do basic things like output a key chord upon a button press using only what's available onboard, sadly. The onboard capabilities are more limited than they have to be, probably to drive people to G-Hub.
https://support.logi.com/hc/en-ca/articles/360059641133-Onbo...