I guess you want to trigger a specific action. No need to popup the context menu: Just post a WM_COMMAND message that matches the context menu item you want to select. You'll find the WM_COMMAND item id associated to the desired menu item using tools such as Spy++ or Winspector.
PostMessage((IntPtr)hWnd, WM_COMMAND, 0, ID_MENU_ITEM);
EDIT: Clarification in answer to your comment:
You send or post the WM_COMMAND message straight to the main window, not to the menu. Actually, you don't need to popup the menu at all. The context menu is just a GUI element that lets the user select an action. The application doesn't need the menu to show up in order to convey said action.