Since the hover color for the items is pulling from the highlight color you would need to remove it from there. Open up your index.php file and look for the following near the top in a long list of CSS items:
#s5_nav li:hover a, #s5_nav li.mainMenuParentBtnFocused a
Also this for the sub menus:
#subMenusContainer li a:hover, .s5_menu_overlay_subs #subMenusContainer li:hover a
You would then need to put this along with your desired hover color in a CSS file.
The background, shadow, etc can all be set in the Vertex admin area under Layout > Menu then scroll down to the floating menu section.