Here in photo 1 you can see the buttons of razer naga mouse
In photo 2 you can see how i change buttons in world of warcraft using Dominios adddon. there I made for convenience, the view of the buttons 3 columns and 4 rows. My fingers remembered the location of the buttons in my mouse in wow. And now I can’t get used to the layout of the buttons in the Blade & Soul 4 columns and 2 rows.
You can't change the internal functioning like that.
What you can do is:
Map the mouse keys as alternative keys, assuming the game will detect the input (it probably won't).
Map the mouse keys to the keyboard keys, with a macro on Razer's software or Autohotkey (not recommended).
You just have to remember where the skills go.
However, I think you can add a 2nd layer of skills, where you can use the extra space as visual help.
I would leave 1-3 as the least used skills, and 10-12 as the most used skills.
I think it is possible to make your own Reshade overlay and show it over the game, where you show where each key is and what it does.