Hi VI,
Long time no see. I hope all is well with you.
I have never used i-web (actually I never heard of it). But I would take a backup of the site using cpanels backup feature (chose "home directory" option). Then extract the backup on my own computer.
Then normally it´s just a matter of removing old sites files through ftp or cpanels file manager or have the help desk clean it out for you.
After that publish new site in the public_html.
As for keeping page urls, as long you name the pages the same, bookmarks should still work.
By the way, I tried sending you a pm that I had moved your post, but it said you could not receive it.