To remove a page tab from a custom menu, you don't delete the page "from the Pages section of your blog's Dashboard", you remove it from the menu in Appearance>Menus.
Now, if I understand correctly, you want a custom list of pages on your sidebar and no page tabs under the header. If so, go to Appearance>Menus, create a menu, name it "Blank" or something like that, add nothing to it, click Save Menu, select it from the pulldown in the Theme Locations module, click Save; then create another menu, name it "Sidebar menu" or something like that, select the pages you want from the Pages module, click Add to Menu, click Save Menu; then go to Appearance>Widgets, add a Custom Menu widget to your sidebar, select Sidebar Menu from the pulldown, save.