There are two options as I see it:
1. These button are standardized.
If so, just test it, and you know which is which.
2. There is no standard.
In that case, offer a settings dialog, where the user can set which button is which.

(The left button may be the right button on left-handed mice.)
I don't think this is true.
A true left-handed mouse probably switched the buttons as well.
In addition, this is something you can change over the mouse settings of the OS.