You could try using this plugin from woothemes called dynamic menus http://docs.woothemes.com/document/woodojo-dynamic-menus/.
This allows to changes menus depending on what page you are viewing. I’m not 100% sure how’d you’d use this to put into a left hand sidebar – but in theory it should work.
The other way to approach this would be use woosidebars and add a custom sidebar to the customize page. Then put a menu into that sidebar.