There are 2 ways this can be done.
Process #1
1) Use the PlusWnd::Browser_GetInterface to get the interface for the Browser.
2) Get the handle of the browser
code:
var hWnd = pPlusWnd.Browser_GetInterface('wBrowser').HWND;
Process #2
Use the FindWindowEx API call until you find the Shell DocObject View window.
Once you have the handle of the browser you can use GetWindowLong to get the style of the window (GWL_STYLE) then remove the WS_EX_RIGHTSCROLLBAR and set the new style and it should be remove.