How to send the right-click event to a tab-chosen control from an application or service?
If you simply want to select GUI elements with keyboard, use Shortcat. It allows you to search all the visible GUI element and select it from your keyboard input.

Another tool you can use to simulate mouse event (such as right click) is Keyboard Maestro. It’s an app to create macro for all kind of events in Mac (from simulating keystrokes, mouse position, and even manipulating clipboard history). You can create almost all kind of interaction with Keyboard Maestro.

By combining those two apps above, you should be able to leave your mouse and trackpad. After all, you are a Keyboard Maestro.