As has been stated before in this thread, it's not possible to call contextual toolbar with right-click.
However, some mouse modifier contexts support setting action to them, so you could assign contextual toolbar action to whichever mouse modifier feels good for you.
I personally use Logitech G602 mouse to which I've assigned various actions, amongst which are contextual toolbars actions.
I have programed these 6 buttons on the side as follows:
2 for contextual toolbars
(one primary, one secondary)
2 for SWS/BR play actions
("perform until shortcut released" versions) to preview things while editing
(whole project and active track only)
2 for undo/redo