You will need to move the call to wp_nav_menu() to sidebar.php to replace wp_list_pages. Depending upon how the theme’s CSS works, you may also have to make some changes to the stylesheet and/or the register_nav_menus() function in functions.php
Well, yes. The point is that simply moving wp_nav_menu() gives me horizontal menu wrapped in several lines instead of vertical menu. So, yes, I could just write my own CSS from scratch for this particular menu.
But I figured that I should be able to somehow tell wp_nav_menu() to use the same CSS that wp_list_pages() uses. Is that possible? Is there a way to make a function wp_list_only_pages_which_are_in_primary_menu() which produces the same results as wp_list_pages()?