Programing mouse for shortcuts in Audacity (Mac)

Is it possible to buy a gaming mouse and program the buttons to help edit in audacity?

Unless you already own a gaming mouse and are thoroughly familiar with using it, you will probably be better off with a normal optical mouse with mouse wheel and your keyboard.
It can take a lot of time and effort to become accustomed to multi-button optical mice, and also note that many gaming mice only have limited functionality on macOS (in most cases the side buttons do nothing).