With WP Menu I guess that you're talking about the main menu. You can personalize your menus if you go to appearance > menus.
Simply give a name to your menus and build your personalized links, in this case anchors
Also, do remember to add the corresponding targets in your page so the anchors in your menu will work
And since this menu will only be valid for this particular page, make sure that it is only active for it. Probably you'll need a plug-in for this
Other options is create some personalized HTML for this page at the top and style it as a menu