Hi,
If you have your home menu item as a hikashop categories listing menu item and that you also have a child menu item of that menu item being also a hikashop categories listing menu item but with the corresponding sub category selected, then I don't see why you would get the "category" piece in the SEF URL. You must have missed something in the settings of the menu items, or you've set a canonical URL in the category with the "category" part in it and you've configured HikaShop to use the canonical URLs on listings.
Removing parts of the URL in the router.php is easy if you're a developer.
At the begining of the function HikashopBuildRoute( &$query ), just remove the bits you don't want in $query.
For example, for category:
if($query['ctrl']=='category') unset($query['ctrl']);
So just look at wat you have in $query with a var_dump() and add the code correspondingly.