if you go Rhinoceros-> Preferences-> Mouse-> Buttons
then click your various mouse buttons while the cursor is over the dialog, do any of the button names (button4, button4, etc) highlight in yellow?
if so, these are the buttons you’ll be able to assign commands to.
in rhino, the left button is already click and the right one is return… for the osnap functionality you’re describing, there’s a mac rhino command _ToggleOsnapPanelUnderCursor …so when you’re in the mouse button preferences, if one of the buttons highlight yellow, put that command in the field for the button then when you click the button in rhino, the osnap panel will toggle on/off under your cursor.
[edit] hmm… just noticed you asked something similar in a Rhino for Windows thread whereas this one is in Rhino for Mac.
are you on mac? if not, ignore the stuff i said earlier 